Driving stability control system with selective brake actuation

ABSTRACT

Apparatus for controlling an automotive vehicle is provided. The vehicle has a plurality of wheels which contact a pavement surface. Each wheel has an individually operable brake. A yawing moment control mechanism determines a moment that is applied to the vehicle to prevent an undesirable yaw angle, yaw rate or yaw acceleration. A slip determining mechanism determines a longitudinal slip value of each of the wheels, individually. A distribution logic mechanism determines an individual braking pressure to be applied to each respective one of the brakes based on the moment. The distribution logic mechanism includes a facility for selectively actuating at least one of the brakes so that the longitudinal slip value of the wheel to which the one brake corresponds is greater than a longitudinal slip value at which the coefficient of friction between the wheel and the surface reaches a maximum value, without actuating all of the brakes at longitudinal slip values above the maximum friction longitudinal slip value.

This application is a division of application Ser. No. 08/475,389, filedJun. 7, 1995.

FIELD OF THE INVENTION

The present invention pertains to a brake system for a motor vehiclewith more than two wheels. The wheels are provided with braking means,which can be actuated independently from one another.

BACKGROUND OF THE INVENTION

1. General Structure of Driving Stability Control (DSC)

Brake systems are used to decelerate the vehicle. By controlling theslip of the individual wheels during braking, it is ensured that thewheels will not be locked, so that the vehicle remains steerable evenduring a braking process.

On the other hand, brake systems are also used to ensure the drivingstability of the vehicle, e.g., during travel in a curve. Drivingstability is defined as the stable movement of the vehicle on a pathpredetermined by the angle of the steering wheel, i.e., a movementwithout excessive rotation around its own vertical axis. To make itpossible to perform the control necessary for this, it is necessary tomeasure the angle of the steering wheel. Taking into account additionaldata, which represent the travel dynamics of the vehicle, it is possibleto derive the curve path on which the driver would like to move thevehicle from the rotation of the steering wheel. A defined yaw rate aswell as a defined side slip angle are associated with this desired curvepath. If the vehicle is to travel through the path in a stable manner,certain limit values of the yaw rate and of the side slip angle must beobserved.

If these limit values are not observed, an additional yawing momentaround the vertical axis of the vehicle (by means of which the desiredyaw rate can be set) can be produced by specifically applying brakeforces acting on one side.

SUMMARY OF THE INVENTION

One method of applying brake forces acting on one side is to trigger thebraking means such that the wheels will be braked at differentintensities. A method by which the brake forces or brake pressures forthe individual braking means are determined from a predeterminedadditional yawing moment will be described in the section "DistributionLogic Unit" below. This method consists essentially of settingcoefficients for each wheel or each braking means, which describe thecontribution of the brake force on that wheel to the total additionalyawing moment, as a function of the brake pressure introduced. Thepressures to be introduced are then determined from the additionalyawing moment to be reached by means of the weighted coefficients.

This method reaches a limit when a driving stability control is to takeplace during braking, i.e., when a certain brake pressure value is setin the wheel brakes based on a deceleration of the vehicle introduced bythe driver. The method outlined above can also be applied, in principle,to this case. Instead of absolute pressures, changes in the brakepressures already set are determined.

However, the following problems occur now. If very high pressures havealready been introduced into the braking means of one wheel, so thatvery strong brake forces are obtained, an increase in the brake pressurewould not necessarily lead to an increase in the brake force, becausethe limit of adhesion between the tire and the road surface has beenreached. However, since the above-mentioned method takes into account alinear relationship between the brake pressure and the brake force, itcan no longer be used in this case.

Instead, the brake force on one side of the vehicle, which is not to beincreased, must be compensated by reducing the brake force on the otherside of the vehicle. This has the same effect with respect to theadditional yawing moment, but it has the disadvantage that thedeceleration of the vehicle is also reduced with the reduction of thebrake force. This is not always acceptable, because the vehicle must bebrought to a stop over the shortest possible distance when a brakingprocess is initiated by the driver. An excessive reduction in the actualdeceleration of the vehicle compared with the deceleration desired bythe driver cannot, in general, be accepted.

The present invention therefore takes a different approach to solve thisproblem. The braking means of at least one wheel is actuated. Thelongitudinal slip of the wheel is adjusted such that it is greater thanthe longitudinal slip at which the maximum frictional connection isreached. This method utilizes the fact that the transmitted brake force,i.e., the longitudinal force acting on the tire, reaches its maximumvalue at a longitudinal slip of approx. 20% (0%=freely rolling wheel;100%=locked wheel), and the brake force that can be transmitteddecreases only slightly at values exceeding 20%, so that there is noconsiderable loss during the deceleration of the vehicle in the case ofa wheel slip between 20% and 100%.

However, a simultaneous consideration of the lateral force that can betransmitted (i.e., the force acting at right angles to the plane of thewheel) shows a strong dependence on the longitudinal slip, in that thelateral force that can be transmitted greatly decreases with increasinglongitudinal slip. In the longitudinal slip range of 50% to 70%, thewheel displays a behavior similar to that of a locked wheel. This meansthat no substantial lateral forces are applied any more, which bringsabout a rotation of the vehicle around its vertical axis.

Controlled swerving of the vehicle can be induced by the selection ofthe wheels as described below, on which a high longitudinal slip valueis set at least briefly, in which case the change in the yaw angle,which is brought about by the swerving, corresponds to the desiredchange. Since the longitudinal forces are essentially preserved in thismethod, but the lateral guiding forces are markedly reduced, the yawrate can be controlled without excessively reducing the deceleration ofthe vehicle.

The selection of the wheel, which is traveling with an increasedrotational slip at least briefly, is performed according to thefollowing rules: Let us examine travel through a curve to the right,which is intended by the driver. Corresponding "mirror-image" rulesapply to travel through a curve to the left. It may happen that thevehicle does not turn into the curve as sharply as expected. In otherwords, the vehicle is understeered. The rear wheel that is the insidewheel in the curve is operated with increased slip values in this case.

However, if the vehicle turns too sharply into the curve, which case iscalled oversteering, the front wheel that is the outer wheel in thecurve is operated with high slip values.

In addition, pressure buildup on a front wheel can be prevented fromoccurring. This is done according to the following rules. Brake pressureis prevented from building up on the front wheel that is the outer wheelin the curve in a driving situation, in which the vehicle displaysundersteered behavior. The pressure is prevented from building up on thefront wheel that is the inner wheel in the curve in a situation in whichthe vehicle displays oversteered behavior.

The actual control of the brake pressure can be performed as follows. Asis explained in section 3 of the description, "Distribution Logic Unit,"the brake pressure in the individual wheel is determined as a functionof the torque to be reached and of weighted wheel coefficients.

When calculating the coefficients, it is possible to introduce a factorthat depends on the wheel slip during braking, and this factor isadjusted such that the above-described desired longitudinal slip isestablished. The pressure buildup on one wheel can be limited by settinga lower threshold for the corresponding coefficient.

BRIEF DESCRIPTION OF THE FIGURES

How such a driving stability control system may be designed is describedbelow on the basis of 29 figures. The objects of the individual figuresare as follows:

FIG. 1 shows a block diagram of the overall structure of a drivingstability control system,

FIG. 2 shows a block diagram of the structure of a yawing momentcontroller,

FIG. 3 shows a flow chart of the determination of a driving situation,e.g., travel in a curve,

FIGS. 4 and 5 show a flow chart of the determination of the coefficientof friction of the road surface, wherein FIG. 5 is to be inserted intoFIG. 4,

FIGS. 6 and 8 show block diagrams of a combined process for determiningthe current values of the velocity of the side slip angle and of theside slip angle in different forms of representation,

FIG. 7 shows a block diagram of the direct determination of the velocityof the side slip angle from kinematic considerations as part of thecombined process according to FIG. 6,

FIG. 9 shows a control circuit for driving stability control with atravel speed-dependent change of the calculation model for the vehicle,

FIG. 10 shows a diagram for describing time intervals within acalculation loop,

FIG. 11 shows a schematic block diagram for determining the wheel brakepressure,

FIGS. 12 and 13A and 13B show diagrams from which the dependence of theking pin inclination difference of a vehicle on the side slip angle andon the velocity vector of the individual wheels can be determined,

FIGS. 14 through 17 show a block diagram of a control circuit forcontrolling the driving stability, in which the variables compared witheach other in the comparison unit are derivations of the yaw rate,

FIG. 18 shows a control circuit for determining the driving stability,in which the pressure gradient and/or the valve-closing time of thevehicle brake is used as the controlled variable,

FIG. 19 shows a block diagram for describing the controller forcalculating the additional yawing moment,

FIG. 20 shows a block diagram for describing a low-pass filter,

FIG. 21 shows a flow chart for calculating a corrected desired yaw rate,

FIG. 22 shows a block diagram for calculating a corrected additionalyawing moment,

FIG. 23 shows a schematic representation of a motor vehicle,

FIG. 24 shows a block diagram for describing the distribution logicunit,

FIG. 25 shows a schematic representation of a motor vehicle and theforces acting on it with the steering wheel turned,

FIG. 26 shows a diagram for describing the lateral and longitudinalforce coefficients as a function of the wheel slip,

FIGS. 27A, B show schematic representations of motor vehicles fordescribing the understeering and oversteering behaviors,

FIG. 28 shows a flow chart with a decision logic unit within thedistribution logic unit, and

FIG. 29 shows a block diagram for calculating switching times for inletand outlet valves.

DETAILED DESCRIPTION

A general description of the course of a driving stability control isshown in FIG. 1. The vehicle 1 forms the controlled system.

The variables given by the driver, namely, the driver brake pressureP_(brake) and the steering angle δ, act on the vehicle 1. The variablesresulting from this, namely, the motor moment M_(motor), the lateralacceleration a_(trans), the yaw rate Ψ, the wheel speeds and hydraulicsignals, such as wheel brake pressures, are measured on the vehicle. Toevaluate these data, the DSC system has four electronic controllers 7,8, 9 and 10, which are associated with the anti-locking system ABS, thetraction slip control system TSC, the electronic brake effortproportioning system EBV, and the yawing moment control system YMC,respectively. The electronic controllers for ABS 7, TSC 8 and EBV 9 maycorrespond to the state of the art without change.

The wheel speeds are sent to the controllers for the anti-locking system7, the traction slip control system 8 and the electronic brake effortproportioning system 9. The controller 8 of the traction slip controlsystem additionally receives data on the actual engine torque, the motormoment M_(Motor). This information is also sent to the controller 10 forthe yawing moment control system YMC. In addition, controller 10receives the data on the lateral acceleration a_(trans) and the yaw rateΨ of the vehicle from the sensors. Since a vehicle reference velocityv_(Ref), on the basis of which an excess brake slip of one of the wheelscan be determined, is determined in the controller 7 of the ABS via theindividual wheel speeds of the vehicle wheels, such a reference velocitydoes not need to be calculated in the YMC controller 10, but it is takenover from the ABS controller 7. Whether the vehicle reference speed iscalculated or a separate calculation is performed for the yawing momentcontrol makes only a slight difference for the process of the yawingmoment control. This also applies, to the longitudinal accelerationa_(long) of the vehicle. The value for this also can be determined inthe ABS controller 7, and sent to the YMC controller 10. This applies tothe determination of the coefficient of friction μ of the road surfacewith restrictions only, because a more accurate coefficient of frictiondetermination than is determined for the anti-locking system isdesirable for yawing moment control.

All four electronic controllers of the DSC, i.e., the controllers forYMC 10, ABS 7, TSC 8 and EBV 9, develop brake pressure set valuesP_(YMC), P_(ABS), P_(TSC), P_(EBV) for the individual wheelssimultaneously and independently from one another based on their owncontrol strategies.

In addition, preset values M_(TSC) and M_(AdjustM) for the engine torqueare calculated by the TSC controller 8 and the YMC controller 10simultaneously.

The pressure preset values p_(YMC) of the YMC controller 10 for theindividual wheel brake pressures are determined as follows: The YMCcontroller 10 first calculates an additional yawing moment M_(G), whichleads to stabilization of the driving condition within a curve if it isgenerated by a corresponding brake actuation. This M_(G) is sent to adistribution logic unit 2, which could also be represented as part ofthe YMC controller 10. In addition, the possible desire of the driver todecelerate the vehicle, which is recognized from the driver brakepressure p_(brake), is also sent to this distribution logic unit 2. Thedistribution logic unit 2 calculates yawing moment control brakepressures p_(YMC) for the wheel brakes, which may differ from the presetyawing moment M_(G) and the desired driver brake pressure very greatlyfor the individual wheels. These yawing moment control brake pressuresP_(YMC) are sent to a priority circuit 3 for the wheel brake pressures,for function optimization along with the pressure preset valuescalculated by the other controllers 7, 8 and 9 for ABS, TSC and EBV.This priority circuit 3 determines desired wheel pressures p_(Desired)for optimal driving stability, taking into account the driver's desire.These desired pressures may either correspond to the pressure presetvalues of one of these four controllers, or represent a superimposition.

The procedure followed in the case of the engine torque is similar tothe procedure with the wheel brake pressures. While ABS and EBV act onlyon the wheel brakes, intervention with the engine torque is alsoprovided in the case of YMC and TSC. The preset values M_(AdjustM) andM_(TSC) calculated separately for the engine torque in the YMCcontroller 10 and in the TSC controller 8 are again evaluated in apriority circuit 4 and superimposed to a desired torque. However, thisdesired torque M_(Desired) may also just as well correspond only to thecalculated preset value of one of the two controllers.

Driving stability control by intervention with the brakes and the enginecan now be performed based on the calculated desired preset values forthe wheel brake pressure P_(Desired) and for the engine torqueM_(Desired). Hydraulic signals or values, which reflect the actual wheelbrake pressure, are also sent for this purpose to the pressure controlunit 5. From this, the pressure control unit 5 generates valve signals,which are sent to the control valves of the individual wheel brakes inthe vehicle 1. The engine management controls the drive motor of thevehicle according to M_(Desired), as a result of which a changed motormoment is again generated. This will then again lead to new inputvariables for the four electronic controllers 7, 8, 9 and 10 of the DSCsystem.

2. Structure of the Yawing Moment Control System (YMC)

FIG. 2 shows in a block diagram how the additional yawing moment M_(G)is determined within the YMC controller 10 for the distribution logicunit 2. The steering angle δ, the vehicle reference velocity v_(Ref)from the ABS controller 7, the measured lateral acceleration a_(trans),and the measured yaw rate Ψ_(Meas) are entered for this as inputvariables. The vehicle reference velocity v_(Re) f passes through afilter 17, which sets a constant value above zero at low velocities, sothat the denominator of a fraction will not become equal to zero duringthe further calculations. The unfiltered value of v_(Ref) is sent onlyto an activation logic unit 11, which recognizes the standstill of thevehicle.

This direct determination of the vehicle reference velocity v_(Ref) bythe activation logic unit 11 may also be omitted if standstill of thevehicle is assumed when the filtered vehicle reference velocityv_(RefFil) assumes its constant minimum.

A vehicle reference model 12, which calculates a preset value for achange in the yaw rate ΔΨ on the basis of the steering angle δ, thefiltered vehicle reference velocity v_(RefFil) as the measured yaw rateΨ_(Meas), is placed in the YMC controller.

To keep the preset values within the physically possible range, thecoefficient of friction μ of the road surface, which is calculated as anestimated value μ in a coefficient of friction and situation recognitionunit 13, is also needed for these calculations. If the coefficient offriction determined within the framework of the anti-locking control hassufficient accuracy, this coefficient of friction may be used as well,or the coefficient of friction calculated in the YMC controller 10 maybe taken over in the ABS controller 7.

The coefficient of friction and situation recognition unit 13 uses forits calculations the filtered reference velocity v_(RefFil), themeasured vehicle lateral acceleration a_(trans), the measured yaw rateΨ_(Meas) and the steering angle δ.

The situation recognition unit distinguishes different cases, such asstraight travel, travel in curves, reverse travel and standstill of thevehicle. Standstill of the vehicle is assumed when the filtered vehiclereference velocity v_(RefFil) assumes its constant minimum. Thisinformation may also be sent to the activation logic unit 11 torecognize standstill of the vehicle instead of the unfiltered vehiclereference velocity. The fact that at a given steering angle δ, theorientation of the measured yaw rate Ψ is opposite that during forwardtravel is utilized to recognize reverse travel. The measured yaw rateΨ_(Meas) is compared for this purpose with the desired yaw rateΨ_(desired) preset by the vehicle reference model 12. If the signs arealways opposite, and this also applies to the time derivatives of thetwo curves, the vehicle is traveling in reverse, because Ψ_(desired) isalways calculated for forward travel, since the usual speed sensors donot detect information on the direction of rotation of the wheels.

Finally, a kinematic velocity of the side slip angle determination, or akinematic determination for short, is performed on the basis of thefiltered vehicle reference velocity v_(RefFil), the measured vehiclelateral acceleration a_(trans), and the measured yaw rate Ψ_(Meas).

To cut off peaks in the case of great variations in the side slipangles, the calculated value of velocity of the side slip angle passesthrough a first-order low-pass filter 15, which sends an estimated valueβ for the velocity of the side slip angle to the activation logic unit11 and to a program 16 for converting the yawing moment control law.Program 16 also uses the preset values for changing ΔΨ for the yaw rate,which is the difference of the measured yaw rate Ψ_(Meas) and thedesired yaw rate Ψ_(desired) calculated on the basis of the vehiclereference model 12. The additional yawing moment M_(G) for the vehicle,which is to be mediated via the brake pressures, is calculated fromthis.

The program 16 operates permanently to keep ready current controlvariables all of the time. However, whether these controlling torquesare transmitted to the distribution logic unit 2 shown in FIG. 1 dependson the activation logic unit 11.

The activation logic unit 11 receives not only the value of theunfiltered vehicle reference velocity v_(Ref) and, as was described, thevelocities of the side slip angles β, but also the amount of thedeviation |ΔΨ| of the desired yaw rate Ψ_(desired) from the measured yawrate Ψ_(Meas), and information from the situation recognition unit 13during reverse travel.

If the vehicle is traveling in reverse, the transmission of M_(G) isinterrupted. This also happens when standstill of the vehicle isrecognized or when neither the estimated velocity of the side slip angleβ nor the preset value for the change in the yaw rate, ΔΨ, reaches avalue that would make control necessary.

The logic circuit for calculating the engine controlling torqueM_(AdjustM) is not shown.

2.1. Coefficient of Friction and Situation Recognition

The logic processes taking place in the coefficient of friction andsituation recognition unit 13 are shown in the form of flow charts inFIGS. 3, 4 and 5.

FIG. 3 pertains to the situation recognition. Eight different drivingsituations can be distinguished with the process shown:

<0> Standstill of the vehicle

<1> Constant straight travel

<2> Accelerated straight travel

<3> Decelerated straight travel

<6> Reverse travel

<7> Constant travel in curve

<8> Accelerated travel in curve

<9> Decelerated travel in curve.

Logic branchings are represented as blocks in the flow chart.

Based on a given situation 51 to be determined, it is first determinedin block 52 whether or not the vehicle is at a standstill. If thefiltered vehicle reference velocity v_(RefFil) assumes its minimumv_(min), standstill of the vehicle, i.e., situation <0>, is assumed. Ifv_(RefFil) is greater than v_(min), the result of the preceding run ofsituation recognition is polled in block 53.

If the situation last determined was recognized as reverse travel, i.e.,situation <6>, reverse travel continues to be present, becausestandstill of the vehicle did not occur in the meantime, becausesituation <0> would have otherwise been recognized in block 52 in themeantime.

If the preceding run of the situation recognition recognized a situationother than <6>, the value of the lateral acceleration a_(trans) ispolled in block 54. If this is lower than a defined threshold valuea_(transmin), it is assumed that the vehicle is traveling straight,i.e., that one of the situations <1> through <3> prevails. This is alsotrue when the value of the measured lateral acceleration a_(trans) isabove the threshold value a_(transmin), but it is recognized in block 55in the next step that value of the steering angle δ is lower than athreshold value δ_(min). The measured lateral acceleration a_(trans) isan error of measurement that results from the fact that lateralacceleration meters are usually securely mounted in the transverse axisof the vehicle and are tilted with the vehicle in the case of aninclination of the road surface, so that a lateral acceleration thatdoes not actually occur is indicated.

Consequently, if the vehicle is traveling straight, the value of thelongitudinal acceleration a_(long) is examined in block 59. If this islower than a threshold value a_(longmin), constant straight travel isassumed. However, if the value of the longitudinal acceleration a_(long)is greater than this threshold value, block 60 makes a distinctionbetween positive and negative longitudinal acceleration. If the value ofa_(long) is above the threshold value a_(longmin), the vehicle is in anaccelerated straight travel, i.e., in situation <2>. If the value ofa_(long) is below the threshold value a_(longmin), this means nothingelse but negative longitudinal acceleration, e.g., decelerated straighttravel, namely, situation <3>.

If none of the situations <0> through <3> occurs and a steering anglevalue that is greater than the threshold value δ_(min) is recognized inblock 55, a polling is performed in block 56 to determine whether thevehicle is currently traveling in reverse. The recognition of reversetravel is necessary only at this point, because the yaw rate Ψ hardlydiffers from zero during straight travel anyway, and no controlintervention is therefore performed. Reverse travel must be ruled outwith certainty only when travel in a curve is recognized, in which theyawing moment control itself becomes active. This is not possible basedsolely on the signals of the wheel speed sensors, because such sensorsonly transmit the value of the speed, without making it possible toinfer the direction of travel from it.

As was described above, situation <6> is determined by comparing themeasured yaw rate Ψ_(Meas) with the desired yaw rate Ψ_(desired)determined in the vehicle reference model 12. If the signs are opposite,and if this is also true of the time derivatives of the two variables,namely, the yaw acceleration Ψ_(Meas) and Ψ_(desired), the vehicle is ina curve, traveling in reverse. The signs of the yaw accelerations aretherefore compared, to rule out that the opposite signs of the yaw ratesoriginate not only from a phase shift, which is due to the time-delayedcalculation of the desired values.

If the conditions for reverse travel are not satisfied, there is travelin a curve in the forward direction. Whether or not this travel in thecurve takes place at constant velocity is investigated in block 57. Aswas done before in blocks 59 and 60 in the case of straight travel, thevalue of the longitudinal acceleration a_(long) is first examined inblock 57. If it is lower than the threshold value a_(longmin), there isconstant travel in a curve, i.e., situation <7>. In the case oflongitudinal acceleration a_(long) whose value is greater than thethreshold value a_(longmin), it is further examined in block 58 whetherthe longitudinal acceleration a_(long) is positive or negative. Thevehicle is in an accelerated travel in a curve, i.e., situation <8>, inthe case of positive longitudinal acceleration a_(long), while adecelerated travel in a curve, corresponding to situation <9>, isrecognized in the case of negative longitudinal acceleration a_(long).

The longitudinal acceleration a_(long) can be recognized in differentways. It can be determined, e.g., from the reference velocity v_(Ref)provided by the ABS controller 7, in which case it should be borne inmind that such a reference velocity v_(Ref) may deviate from the actualvehicle velocity during an ABS intervention. Consequently, a correctionof v_(Ref) is justified in an ABS case. However, the longitudinalacceleration a_(long) can also be taken over under certain circumstancesdirectly from the ABS controller if such calculation is performed there.

The situation recognition according to FIG. 3 is continually run throughagain, and the situation last determined remains stored and is availablein block 53.

A possible process for determining the coefficient of friction of theroad surface is shown in FIGS. 4 and 5. According to this process, thecoefficient of friction is determined only when the yawing momentcontroller enters the control. However, since no estimated coefficientof friction is still available at the time of entry into the control,the coefficient of friction μ=1 is set at the beginning of the control.

If the yawing moment control system responds on the basis of aninstantaneous driving situation, it can be assumed that the vehicle isat least in the vicinity of the borderline range to unstable drivingsituations. The instantaneous coefficient of friction of the roadsurface can therefore be inferred from an examination of the currentmeasured variables of the vehicle. The coefficient of friction thendetermined at the time of entry into the control will subsequently serveas the basis for limiting the desired yaw rate Ψ_(desired) andconsequently also for the control deviation for the yaw rate ΔΨ, whichis transmitted to the YMC control law unit 16. The coefficient offriction is determined for the first time at the time of entry into thecontrol, associated with a subsequent phase of updating for thelimitation of the desired yaw rate to physically meaningful values.Based on the originally preset coefficient of friction μ=1, a maximumcoefficient of friction μ is determined at the time of entry into thecontrol, and the calculation of the additional yawing moment M_(G) willthen be based on this value.

An internal coefficient of friction μ_(int) first determined for thisfrom the measured lateral acceleration a_(trans) and a calculated valuefor the longitudinal acceleration a_(long), which value corresponds tothe instantaneous coefficient of friction if complete utilization of thefrictional connection is assumed. However, since it must be assumed thatthe maximum frictional connection is not yet reached at the time ofentry into the control, a higher coefficient of friction μ is associatedwith the internal coefficient of friction μ_(int) by means of a table, acharacteristic curve or a constant factor. This coefficient of frictionμ is then sent to the control system. It is thus possible to calculatewith a desired yaw rate Ψ_(desired) adjusted to the coefficient offriction of the road surface in the next step of the calculation and toimprove the control. While the yawing moment control system acts on thevehicle, the estimated coefficient of friction μ must be furtherupdated, because a change in the coefficient of friction might takeplace during the control. If the control system is not activated basedon the adjustment of the coefficient of friction in the vehiclereference model due to the resulting changed control deviation of theyaw rate ΔΨ, the coefficient of friction μ is further updated inT.sub.μEnd number of steps. If the yawing moment control system is notactivated even during this phase of updating, the estimated coefficientof friction μ is reset to 1.

The adjustment or updating of the estimated coefficient of friction μmay also be omitted in certain situations. Such situations are, e.g.,straight travel, travel in reverse or standstill of the vehicle, i.e.,situations <0> through <4>. These are situations in which no yawingmoment control is performed anyway, so that an estimation of thecoefficient of friction is also unnecessary. Updating the coefficient offriction may be omitted if the time derivative of the coefficient offriction μ, i.e., μ, is negative and the value of the time derivative ofthe steering angle δ, i.e., |δ|, exceeds a predetermined threshold. Itcan be assumed in the latter case that a change in the lateralacceleration a_(trans) is based on a change in the steering angle δ,rather than on a change in the coefficient of friction.

It is generally true of the coefficient of friction calculated in thismanner that it is a mean coefficient of friction for all four wheels ofthe vehicle. The coefficient of friction cannot be determined in thismanner for the individual wheels.

The process of the coefficient of friction determination will now beexplained on the basis of FIG. 4. The behavior of the vehicle isaffected by the prevailing coefficient of friction of the road surfaceaccording to field 61 in each driving situation. To determine thecorresponding coefficient of friction of the road surface, the measuredlateral acceleration a_(trans) is first filtered according to step 62,i.e., either the measured values are smoothed, or the curve passesthrough a low-pass filter, so that no extreme peaks appear. Step 63comprises the situation recognition according to FIG. 3. The drivingsituation recognized is later significant for the phase of updating instep 74. A polling is performed in block 64 to determine whether acontrol intervention is necessary. Such a calculation is first based onthe initial coefficient of friction μ=1. If control is considered to benecessary, a polling is performed in block 65 to determine whether thiswas also the condition at the end of the preceding run of thecoefficient of friction determination. If an entry into control isinvolved here, control was not recognized before, so that an internalcoefficient of friction μ_(int) is determined for the first time in step67. It is calculated from the following equation:

F. 2.1 ##EQU1##

Here, g is the gravitation constant g=9.81 m/sec².

The parameter reg_(old) for step 65 is set at 1 in step 68. In addition,the counting parameter Tμ is set at 1, corresponding to the fact thatthe first determination of the internal coefficient of friction μ_(int)has been performed. An estimated coefficient of friction μ is associatedwith the calculated internal coefficient of friction μ_(int) in step 69.This is done under the assumption that the existing accelerationcomponents are not based on a complete utilization of the frictionalconnection, either. The estimated coefficient of friction μ isconsequently usually between the internal coefficient of frictionμ_(int) thus determined and 1. The determination of the coefficient offriction is thus concluded.

Consequently, assuming an unchanged driving situation, reg_(old) =1 isdecided in block 65 during the next run of this coefficient of frictiondetermination. A μ_(int), which replaces the μ_(int) determined in thepreceding run, is later determined here as well. The parametersdetermined in field 68 are not updated, because the updating of μ_(int)was performed during a control. reg_(old) had been set at 1 already inthe run before that, and it remains unchanged. The number Tμ of runsperformed continues to be 1, because counting is continued only if nocontrol takes place. As was described above, an estimated coefficient offriction μ is also associated with the updated value of μ int by meansof a table, a nonlinear relationship, or a constant factor.

If it is determined in one run in block 64 that control is notnecessary, a polling is then performed in block 71 to determine whetherthe parameter reg_(old) for the control was last set at 0 or 1. If itwas set at 1 in the last run, the number Tμ of runs is polled in block72. This T.sub.μ equals 1 if control was performed in the last run. Ifcontrol was performed only in the run before last, T.sub.μ =2, etc. IfT.sub.μ has not yet reached a certain T.sub.μEnd in step 72, it isincreased by 1 in step 73, and a repeated updating of the internalcoefficient of friction μ_(int) is performed in step 74. If the numberT.sub.μEnd is then reached in one of the next runs without controlhaving taken place, the parameter reg_(old) is again reset to 0 for thecontrol. The estimated coefficient of friction μ is equated with theinitial coefficient of friction μ=1. The phase of updating for thecoefficient of friction μ is thus terminated.

If it is then again recognized in the next run in block 64 that nocontrol is necessary, the initial coefficient of friction μ=1 isretained in field 76 in block 71 with reg_(old) =0. A coefficient offriction determination is again performed only if the necessity of acontrol intervention is recognized in field 64.

The criteria for updating the internal coefficient of friction μ_(int)after step 74 are shown in FIG. 5. Based on the instruction in field 77that the internal coefficient of friction μ_(int) is to be updated, thetime derivatives of the estimated coefficients of friction μ or μ_(int)formed before, as well as of the steering angle δ are formed in step 78.When it is then recognized in block 79 that the vehicle is neither at astandstill nor is it traveling straight, i.e., that one of thesituations <6> through <9> occurs, the results from step 78 areevaluated in step 80. A coefficient of friction determination isperformed, as was explained above, only if a decreasing coefficient offriction cannot be attributed to a steering maneuver. No updating of thecoefficient of friction is performed if the vehicle is travelingstraight, forward or in reverse, or if it is at a standstill, or if areduction in the estimated coefficient of friction μ can be attributedto a steering maneuver.

2.2. Determination of β and β

The prevailing side slip angle β as well as its time derivative, thevelocity of the side slip angle β are an indicator of the stability of adriving condition. The determination of these values will be explainedbelow.

2.2.1. Kinematic Determination of β

The kinematic determination of β, 14, is nothing else but thedetermination of the velocity of the side slip angle β, separated fromany vehicle model, from measured variables or from variables calculatedon the basis of measured values, according to purely physicalconsiderations:

The acceleration a_(trans) of the center of gravity of the vehicle atright angles to its longitudinal axis in the plane of movement ismeasured. The center of gravity of the vehicle moves with the velocityvector v relative to an inertial system:

F 2.2 ##EQU2##

The yaw angle is designated by Ψ and the side slip angle by β. Theacceleration vector a is obtained as a derivative over time t as:

F 2.3 ##EQU3##

The acceleration sensor measures the projection of the accelerationvector to the transverse axis of the vehicle:

F 2.4 ##EQU4## F 2.5

    a.sub.trans =ν sin β+v·(Ψ+β) cos β

After linearization of the trigonometric functions (sin β=β; cos β=1),the equation can be rewritten as

F 2.6 ##EQU5##

The velocity of the side slip angle β corresponding to the abovedifferential equation can now be calculated. Besides the lateralacceleration a_(trans), the yaw rate Ψ, the scalar velocity of thevehicle v and its time derivative ν are included as measured variables.To determine β, β from the previous calculation can be numericallyintegrated, and ν=0 is assumed for the first determination of β. Asimplification is obtained if the last term is generally ignored, sothat no β needs to be determined.

The proposed procedure offers the advantage that the velocity of theside slip angle β is directly derived from the sensor signals and thusit can also be determined in the nonlinear range of the transversedynamics. The disadvantages are the sensitivity of the procedure tomeasurement noise and the cumulative integration of errors ofmeasurement, as a result of which the determination of the side slipangle may become highly inaccurate.

These disadvantages are circumvented by the combination with amodel-supported procedure. FIG. 6, which can be inserted in place of theblock 18 drawn in broken line in FIG. 2, shows such a combination of thekinematic determination with the observer model-supported determinationof the velocity of the side slip angle β. The steering angle δ, which isindicated by an arrow drawn in broken line, is also included as anadditional input variable in such a model-supported procedure. Themutual influences and correction of the combined methods ofdetermination of the velocity of the side slip angle β also make itpossible to calculate the side slip angle β itself with less error, sothat it can then also be made available to the control as β. This isalso indicated by an arrow drawn in broken line.

2.2.2. Combination of the Kinematic Determination of β with an ObserverVehicle Model

The area 18 bordered in broken line in FIG. 2 can also be replaced withthe representation according to FIG. 6. It will thus become possible todetermine not only the existing velocity of the side slip angle β, butalso the prevailing side slip angle β.

Contrary to a purely kinematic calculation of the velocity of the sideslip angle β, an observer vehicle model 84 is used here to determine thedriving condition, in addition to the kinematic determination of β. Justlike the vehicle reference model 12 for determining the yaw rate, theobserver vehicle model 84 receives the steering angle δ as the inputvariable. The filtered vehicle reference velocity v_(RefFil) is includedas a parameter. The measurable output variables, namely, the lateralacceleration a_(trans) and the yaw rate Ψ_(Meas), are needed for thekinematic determination of β, 83, but not for the observer vehicle model84, which creates these variables, in principle, itself.

Another term Y, which is identical in the simplest case to theadditional yawing moment calculated by the control law unit, representsthe changes in the vehicle behavior, which are caused by a controlintervention. Y is also used to expose the observer's simulated vehicleto the same conditions as the real vehicle.

Besides a velocity of the side slip angle β_(Obs), the observer vehiclemodel also gives a value for the yaw acceleration Ψ_(Obs). The variablefor the velocity of the side slip angle β, which originates from thekinematic determination of β, is multiplied by a weighting factor kafter passing through the low-pass filter, while the variable for thevelocity of the side slip angle β_(Obs), which originates from theobserver vehicle model, is multiplied by a weighting factor (1-k). Thevalue of k is always between 0 and 1. We would have k=1 without theobserver vehicle model. After adding the two velocities of the side slipangles, the sum is integrated into an estimated side slip angle β.Besides the kinematic velocity of the side slip angle β, this is alsomade available to the control. In addition, the side slip angle β istransmitted to both the kinematic determination of β and the observervehicle model 84. A similar correcting variable is the yaw accelerationΨ_(Obs) calculated by the observer vehicle model 84.

This is first integrated to a yaw rate and returns to the observervehicle model 84, on the one hand, and is subtracted from the measuredyaw rate Ψ, on the other hand. This difference is multiplied by a factorh that determines the value of the next control steps in the correctionof the observer vehicle model 84 and is provided with the dimension 1/s.The yaw rate multiplied by this factor h has consequently the samedimension as the yaw acceleration Ψ, so that the two variables can beadded up and form a returning correcting variable for the yaw rate afterfurther integration.

In the course of a yawing moment control, the term Y assumes valuesdifferent from zero, corresponding to the additional yawing moment M_(G)applied. By being divided by the moment of inertia in yaw 0 of thevehicle, the term Y also acquires the dimension of a yaw accelerationand is added to the sum of the yaw accelerations, so that the integratedcorrection variable also takes into account the control effects orinfluences.

If an observer vehicle model 84 according to FIG. 6 is present, whichmakes possible a more reliable determination of the side slip angle βthan would be possible with a purely kinematic determination of thevelocity of the side slip angle β and integration, the side slip angle βthus determined can also be transmitted to the yawing moment controller10 proper.

The kinematic determination of β, which takes place in combination withan observer vehicle model, is shown in FIG. 7. As is apparent even fromFIG. 6, the lateral acceleration a_(trans) and the yaw rate Ψ_(Meas) areincluded in the calculation 91 according to Equation F 2.6 as measuredoutput variables.

The filtered vehicle reference velocity v_(RefFil) is differentiated infield 93 to provide the vehicle reference velocity v_(Ref), which isdivided in field 94 by the filtered vehicle reference velocityv_(RefFil), which leads to a factor f.sub.β after nonlinearmultiplication 95. This nonlinear multiplication 95 leads to the factorf.sub.β being set to equal zero at low quotients of v_(Ref) andv_(RefFil), so that this factor, which precedes the side slip angle β,can be ignored. The side slip angle β is taken into account in thekinematic determination of β only when the vehicle acceleration v_(Ref)reaches a significant value. The β used here is the combined β, which isused both as a variable for the control and for feedback according toFIG. 6. After calculation 91, the value determined for the velocity ofthe side slip angle passes through a low-pass filter 92, as wasdescribed above, and it yields the estimated velocity of the side slipangle β.

FIG. 8 shows how the observer vehicle model 84 from FIG. 6 operates. Amatrix representation was selected, in which "→" are scalar and ""multidimensional formations.

The matrix representation is based on Equations F 1.1 through F 1.3. Thephase variables β and Ψ are combined into a phase vector x(t), so thatthe following set of equations is obtained:

F 2.7

    x(t)=A(v(t))x(t)+B(v(t)) u(t)

with the system matrix A(v(t)), the input matrix B(v(t)), the phasevector x(t) and the input vector u(t):

F 2.8 ##EQU6##

The input vector u(t) contains as the input variables the steering angleδ and the term Y, which is the additional yawing moment generated by theyawing moment control system.

Instead of weighting factors, a weighting matrix k₁ and a weightingvector k₂ are used for the weighted addition of the variablesdetermined.

F 2.9 ##EQU7##

To eliminate the phase variables, two vectors, c.sub.β and c.sub.Ψ, areintroduced, which cancel one component of the phase vector each:

F 2.10

    c.sub.β = 1,0!; c.sub.Ψ = 0,1!

The dynamics of the observer vehicle model, i.e., the value of thecorrection steps, is determined by a vector h, whose first component,h₁, is dimensionless, and whose second component, h₂, has the dimension(1/s):

F 2.11 ##EQU8##

Based on the vehicle model in the description of the phase space (F 1.1and F 1.2), the structure described below is then obtained fordetermining the side slip angle β by means of an observer according toFIG. 8.

The vehicle 101 is shown in FIG. 8 only to distinguish between inputvariables and output variables. It is not a part of the combinedprocedure for determining the velocity of the side slip angle β.

The system equations according to F 2.7 are formed in the adder 104. Todo so, the system matrix A is multiplied by the phase vector x, and theinput matrix B is multiplied by the input variables and y, i.e., withthe input vector u.

The current vehicle reference velocity v_(RefFil) is included as theonly variable parameter in both the system matrix A and the input matrixB. The time derivative x of the phase vector x, formed in the adder 104by addition, is now multiplied by the weighting matrix K₁ according to F2.9 and is sent to another adder 105.

Simultaneously to these processes, a velocity of the side slip angle βis estimated in the direct procedure 103. The filtered vehicle referencevelocity v_(RefFil), as well as its time derivative v_(Ref), determinedin the differentiator 102 (identified by 93 in FIG. 7), the measuredlateral acceleration a_(trans), as well as the measured yaw rateΨ_(Meas) according to Equation F 2.6 are used for this. The last term ofthe equation is ignored in the first step, because no value of the sideslip angle β is available as yet. After the velocity of the side slipangle is determined, it still passes through the low-pass filter 92, aswas shown in FIG. 7, after which the resulting estimated velocity of theside slip angle β is made available for the further calculation. This βcorresponds to the β which is output from the shaded field in FIG. 2.The scalar β is multiplied by the weighting factor k₂, so that a vectoris obtained from this, whose first component has the dimension of anangular velocity, and whose second component equals zero. This vector isalso sent to the adder 105. The vector resulting from the sum of thetime derivative x of the phase vector x formed according to Equation F2.7 and of the vector obtained from the multiplication with k₂ isintegrated in the integrator 106 into the phase vector x. One of thecomponents β and Ψ is eliminated from the phase vector by scalarmultiplication of the vectors c.sub.β and c.sub.Ψ and is furtherprocessed. While the estimated is sent to the YMC control law unit 16,on the one hand, and to the direct process 103, on the other hand, thecalculated is used within the combined process only as a state variablewithin the observer and for determining the error of estimation. Thedifference between the yaw rate Ψ determined from the observer vehiclemodel and the measured yaw rate Ψ_(Meas) is formed for this purpose inthe adder 107. This difference is multiplied by a vector h, whose firstcomponent is dimensionless and sets the value of the correction stepsfor the velocity of the side slip angle β, and whose second componenthas the dimension s⁻¹ and determines the value of the control stepsduring the correction of the yaw rate Ψ.

The side slip angle β is also returned as a correcting variable;specifically, it is fed back into the direct procedure of the kinematicdetermination of β according to FIG. 7, so that the last term ofEquation F 2.6 can also be assigned a value in the subsequent controlstep.

A substantially more accurate determination of the side slip angle β ispossible due to the mutual correction of the two calculation procedures,i.e., the calculation on the basis of a vehicle model and thecalculation on the basis of kinematic considerations, so that this sideslip angle can also be sent as a controlled variable to the YMC controllaw unit 16.

2.3. Vehicle Reference Models

The vehicle reference model will be explained below on the basis ofFIGS. 9 and 12 through 17.

FIG. 9 shows an even more simplified version of the control circuitaccording to FIG. 1 and FIG. 2 for controlling the driving stability ofa vehicle. The controllers 7 through 9 in FIG. 1, the correspondingpriority circuit 3 and the motor management 6 are omitted, and thedistribution logic unit 2 is shown combined with the pressure controlunit 5. An additional yawing moment M_(G) around the vertical axis iscalculated and set within the control circuit, so that the curve pathdesired by the driver is maintained. The additional yawing moment M_(G)is generated by specific braking processes on the individual wheels, andthe course of the braking processes and the selection of the wheels tobe braked are set by the distribution logic 2. The desired direction oftravel is set by the driver by selecting a corresponding angularposition of the steering wheel. The steering wheel is coupled with thesteered wheels at a fixed transmission ratio (steering ratio). A definedsteering angle δ of the wheels is thus set.

2.3.1. Dynamic Single-Track Model

A so-called vehicle reference model 12 (FIG. 2)=302 (FIG. 9), which issupplied with input data (velocity v, represented by v_(Ref), steeringangle), is provided in the YMC controller 10. The size of the change inthe yaw angle (yaw rate Ψ_(Desired)) is calculated in the vehiclereference model 302 on the basis of the input data. The desired value ofthe yaw rate Ψ_(Desired) is compared with the measured actual value ofthe yaw rate Ψ_(Meas) in a downstream comparison unit 303. Thecomparison unit 303 sends as an output value an output variable ΔΨ,which corresponds to the difference between Ψ_(Desired) and Ψ_(Meas).The difference value thus determined is sent to a control law unit 16for controlling the yawing moment. On the basis of ΔΨ, the control lawunit calculates an additional yawing moment M_(G), which is sent to thedistribution logic unit 2. Based on the additional yawing moment M_(G)and possibly the driver's desire to build up pressure in the brakes,p_(Brake), the distribution logic unit 2 sets output variables. Thesemay be brake pressure values or valve switching times.

Optimal mode of operation of the vehicle reference model 302 is alsoimportant in the range of low velocities. To ensure this, the vehiclereference model 302 may also be provided with a stationary circulartravel model 306, in addition to the above-described linear dynamicsingle-track model 311.

For the stationary circular travel:

F 2.12 ##EQU9## F 2.13 ##EQU10## in which F 2.14 ##EQU11##

Here, v=front; h=rear; m=weight; l=distance between the axle and thecenter of gravity; Ψ_(korr), β_(korr) =correction terms for, Ψ, βrespectively.

The system equations F 1.1 and F 1.2 are valid for the linear dynamicsingle-track model.

The switching over between the calculation models 306 and 311 isperformed automatically by a change-over switch (not shown in thedrawing) in the vehicle reference model 302 as a function of thevelocity of the vehicle. A hysteresis of a few km/h is provided forswitch-over processes from one model to the other. Below the switchingthreshold, the desired yaw rate Ψ_(Desired) is calculated according tothe model of stationary circular travel. If the velocity, increasingfrom a lower value, exceeds the threshold that applies to thisdirection, the calculation of the desired value of the yaw rateΨ_(Desired) is performed by means of the dynamic single-track model 311.The dynamic processes that are particularly important for control athigher velocities are thus incorporated in the model.

The desired values calculated by the circular travel model, such asΨ_(Desired) and β, are used as the starting values for the single-trackmodel when switching over from the circular travel model 306 to thesingle-track model 311. As a result, transient effects duringswitch-over are avoided. Further calculation is performed by means ofthe single-track model 311 until the velocity drops below the velocitythreshold, which is lower for decreasing velocity. To minimize transienteffects here as well, the correction factors Ψ_(korr) and β_(korr)necessary for the circular travel model are calculated with the valuesfor Ψ_(Desired) and β, which were calculated before in the single-trackmodel, as well as with the velocity v_(Ref) and the steering angle δ asthe input variables.

The correction values are as follows:

F 2.15 ##EQU12## F 2.16 ##EQU13##

The effect of these correction factors decreases exponentially over timeaccording to the equation:

F 2.17

    Ψ.sub.korr (n+1)=Ψ.sub.korr (n)*λ

    β.sub.korr (n+1)=β.sub.korr (n)*λ

in which λ may assume values between 0 and less than 1. The calculationruns are counted with n and n+1.

Sudden changes are avoided as a result, because the two calculationmethods yield different results in the stationary case. Thus, thechangeover between calculation models offers the possibility ofdetermining the desired values for the control system at a rather highaccuracy to velocities of v=0 km/h.

It was explained in connection with FIG. 9 that different models can beconsidered for use as vehicle calculation models. The stationarycircular travel may be a preferred model. The yaw rate Ψ_(Desired) canbe calculated according to this model from the above formula. If such avehicle calculation model is to be represented, it is possible to sendthe measured values and v_(Ref) to a calculation circuit 350 and tosubsequently poll the desired value of the yaw rate Ψ_(Desired) as anoutput value.

2.3.2. Simplified Model

An extremely simple model for determining a desired yaw rate will bedescribed below. It shall be an alternative to the above-describedcombination model. It is characterized in that an acceptable result isobtained with a small amount of calculations.

The desired yaw rate Ψ_(Desired) is calculated according to this modelas follows:

F 2.18 ##EQU14##

This equation is obtained from F 2.12, with equations F2.14 and F2.15 ifthe rigidities c_(r) and c₁ are assumed to be very high.

This hypothesis is based on the following considerations.

In the vehicle reference model described above, the desired yaw rateΨ_(Desired) is calculated either by means of a dynamic vehicle model(e.g., a single-track model) or by a static model (called stationarycircular travel value) and is compared with the measured yaw rateΨ_(Meas). However, the preset value (and consequently also the controlintervention) depend directly on the quality of the vehicle model ineach of these hypotheses. Since these are linear equivalent models, themodel markedly differs in some cases from the actual behavior of thevehicle.

If the real behavior of the vehicle additionally changes due to, e.g.,load or wear of individual components, the model describes the vehicleonly insufficiently. Consequently, adaptation of the model should beperformed by means of a continuous parameter estimation, in connectionwith which the following problems arise:

An excitation must be present for the estimation, i.e., the drivershould sufficiently excite the vehicle by means of a steeringinstruction in the linear range (<0.4 g). This hardly applies to normaldriving.

Furthermore, it is not possible to directly estimate all parameters ofthe linear single-track model. Thus, certain parameters should bepreselected as fixed parameters.

Consequently, control on the basis of model hypotheses can always offera satisfactory solution only regarding the model preset values. It maytherefore be sufficient in many cases to proceed according to a simplecontrol principle.

One important goal of driving stability control is to coordinate thedriving behavior such that the response of the vehicle to steering,braking and gas pedal inputs of the driver is always predictable andreadily controllable. Consequently, understeering and oversteeringoperating conditions of the vehicle must be recognized and corrected toneutral behavior by a corresponding braking or engine managementintervention.

The idea of a simplified control principle is that a direct indicator ofthe understeering/oversteering behavior is used as a controlledvariable. According to a definition of the steering behavior of a motorvehicle the mean king pin inclinations of the front axle and rear axle(α_(v), α_(H)) are compared for this purpose. In the case of greaterking pin inclinations of the front axle, the vehicle thus exhibits anundersteering behavior, and, in the opposite case, an oversteeringbehavior. According to the definition, neutral behavior is present ifthe king pin inclinations front and rear are equal. Thus,

F 2.19 ##EQU15##

Based on the difference of the king pin inclinations, it is consequentlypossible to directly determine the instantaneous driving condition ofthe vehicle. If the single-track vehicle model (FIG. 12) is used as ahypothesis, the king pin inclinations can be derived from this as afunction of the steering angle δ, the side slip angle β, the yaw rate Ψand the velocity of the vehicle v, as follows:

F 2.20a ##EQU16## F 2.20b ##EQU17##

Since the side slip angle cannot be directly measured or calculated in asimple manner, an explicit calculation of the individual king pininclinations must be performed. However, if their difference is formed,it is possible to calculate this variable on the basis of the existingmeasured variables (steering angle, yaw rate) of the vehicle referencevelocity v_(Ref) known from the ABS controller and from the constantwheel base 1.

F 2.21 ##EQU18##

Thus, a variable that can be used as an indicator ofundersteering/oversteering is available.

If the known relationship between the instantaneous curve radius R ofthe curve path of the center of gravity of the vehicle and thedifference of the king pin inclinations is also considered

F 2.22 ##EQU19## it can be recognized that if a neutral state of thevehicle (F 2.19) is assumed

F 2.23

    α.sub.ν -α.sub.h =0

the curve radius R can be determined only by the steering angle, namely,

F 2.24

    R=l/δ

A control that directly uses the calculated king pin inclinationdifference as the controlled variable is therefore possible. Theinstruction for this control is to keep the value of this controlledvariable as small as possible in order thus to achieve an approximatelyneutral behavior. It may be meaningful to assume this tolerancethreshold to be asymmetric, so that the tolerance can be selected to besmaller in the direction of oversteering behavior.

The desired yaw rate Ψ_(Desired) can be calculated according to theseconsiderations (F 2.18). This yaw rate Ψ_(Desired) is then compared withΨ_(Meas) and is used as the basis of the control according to FIG. 1.

2.3.3. Desired Value Limitation

Controlling the driving behavior of the vehicle makes sense only as longas the adhesion of the wheels of the vehicle on the road surface permitsthe calculated additional torque to act on the vehicle.

It is undesirable, e.g., for the control to always force the vehicle tothe curve path predetermined by the steering angle δ when the steeringwheel was turned in excessively or too rapidly in relation to theexisting velocity of the vehicle.

Ψ_(Desired) should therefore be prevented from always being selected asthe preset value under all circumstances, according to the vehiclereference model selected, because if the reference model alone isfollowed, it may happen under unfortunate circumstances that if thesteering wheel angle is accidentally set at an excessively high value,and the velocity is also high at the same time, the actual yaw rate Ψwill be changed so much, due to the fact that Ψ_(Desired) is also toohigh in this case, that the vehicle will rotate around its own axis inthe extreme case, while its center of gravity is moving in anessentially straight line at the same time. This condition is even muchmore unfavorable for the driver than the condition in which the vehicleis unable to obey the driver's desire due to the poor frictionconditions and pushes out in a strongly understeering manner, becausethe vehicle will at most only travel straight in this case, without alsorotating around its own axis.

To avoid these consequences, which are disadvantageous in special cases,calculation algorithms, which make it possible to set the maximum yawrate Ψ_(Desiredmax) valid for the velocity just measured via thecoefficient of friction μ, are additionally provided in the vehiclereference model. μ is determined in the coefficient of frictionrecognition unit 13. The calculation algorithms are based on the theoryof stationary circular travel, for which Ψ=a_(trans) /v (F 2.18).

The maximum allowable lateral acceleration a_(qlim) can be determinedessentially as a function of the coefficient of friction, the velocityv, the longitudinal acceleration a_(long), and possibly otherparameters. Thus,

F 2.25

    α.sub.qlim =ƒ(μ, ν,a.sub.long, . . . )

The maximum yaw rate can be calculated as:

F 2.26 ##EQU20##

It is therefore possible to set a limit value for the yaw rate, whichdoes not take the driver's wish directly into account any longer, but itcontributes to preventing the vehicle from additionally rotating aroundits vertical axis when it swings out.

Details of the suitable determination of μ will be described under 2.1.

Provisions can also be made to permit a control intervention only undercertain prevailing conditions. One possibility for this may be, e.g.,for the activation logic unit 11 in FIG. 2 to not transmit any currentM_(G) to the distribution logic unit 2 when an excessively large sideslip angle β is determined, which can happen depending on the justoccurring velocity.

2.4. Control Law Unit

The program structure of the control law unit 16 of the yawing momentcontroller 10 will be described below. From four input variables, theprogram calculates the additional yawing moment M_(G) around thevertical axis of the vehicle that is necessary to obtain a stablevehicle behavior especially during travel in a curve. The yawing momentM_(G) calculated is the basis for the calculation of the pressures to beapplied to the wheel brakes.

The following input variables are available for the control law unit(see FIG. 19):

at input 500: ΔΨ

at input 501: ΔΨ

at input 502: β

at input 503: β

If the king pin inclination difference is used as a basis, ΔΨ is presentat the input 500 and ΔΨ is present at the input 501.

Input 503 is facultative. It is available especially when a so-calledobserver vehicle model 84 is provided in the overall calculation system.

The value at input 500 is obtained as the difference between themeasured yaw rate Ψ_(Meas) and the desired yaw rate Ψ_(Desired)calculated by means of a vehicle reference model 12.

The value at input 501 is obtained either as a change in the variable atinput 500 over time from one calculation loop to the next, divided bythe loop time T₀, or as a difference between the time derivative of themeasured yaw rate and the time derivative of the calculated desired yawrate.

A calculation loop is defined as a calculation run through the DSCdriving stability controller according to FIG. 1. Due to its structure,such a loop requires a certain amount of real time, the loop time T₀.This must be kept sufficiently short for an effective control.

The values at the inputs 500 and 501, namely, ΔΨ and ΔΨ, are first sentto a respective low-pass filter 510 or 511.

The two low-pass filters are, in principle, of the same design, and havethe structure shown in FIG. 20.

The input variable 520 of the low-pass filter according to FIG. 20 isdesignated by u, and the output variable 521 is designated by y. Theoutput variable 521 is sent to a register 522 and is available as aprevious value y(k-1) at the time of the next calculation. The outputvalue 521 for the calculation loop can then be calculated according tothe formula

F 2.27

    y(k)=λ*y(k-1)+(1-λ)*u*k.sub.p

in which λ may assume values between 0 and 1. λ describes the quality ofthe low-pass filter. The recursion function is eliminated at the limitvalue λ=0: The previous values y(k-1) are of no significance for thecalculation of the new output value 521. The more closely λ approachesthe value of 1, the stronger will be the effect of the previous values,so that the current input value 520 becomes established as an outputvalue 521 only slowly.

k_(p) is a linear rating factor.

The low-pass filtration just described is performed for both inputvalues 500 and 501, and it leads to filtered values 515, 516.

An identical low-pass filtration 512 is performed for the input variable502, namely, β. The filtered value 517 is sent, just as the unfilteredvalue 503, to nonlinear filters 523,524. These filters 523,524 have thetask of setting the output value to 0 for low input values and oftransmitting an input value reduced by the limit value for input valuesthat are above a certain limit value.

The limitation is performed in the negative and positive ranges alike.The limit values β_(th) and β_(th) may be fixed values implemented inthe program, but they may also be variables that depend on otherparameters, e.g., the coefficient of friction between the tires and theroad surface. The limit values are calculated separately as a linearfunction of the coefficient of friction in this case.

All four variables, namely, 515, 516, 518 and 519, are weighted with alinear factor each in a next step 530, 531, 532 and 533, respectively.

These factors are implemented as fixed values in the calculation system.They can be calculated, in terms of their order of magnitude, fromcorresponding vehicle models, but they need, in general, a fineadjustment by driving tests. A corresponding set of linear factors isthus set for each vehicle or for each model of vehicle. The inputvariables 500, 501, 502, 503 thus weighted are added up, and (additionmember 540) the additional yawing moment M_(G) is obtained, which isused as the basis for the further calculation process of the program.

However, it was found in practice that modifications of the calculatedyawing moment are still necessary.

Two hypotheses can be made for this:

1. The input variables, especially ΔΨ, are modified.

2. The calculated yawing moment M_(G) is subjected to filtration.

Attempts are made with both statements to perform the control not onlyin consideration of the yaw rate, but also in consideration of the sideslip angle.

2.4.1. Modification of the Input Variables

As was explained, a desired value is calculated for the yaw rate bymeans of a vehicle reference model. Since the vehicle reference modelcannot completely agree with the actual conditions, it is usuallynecessary to correct the result of the model calculation once again. Thevalues which are provided by a yaw rate sensor, as well as a steeringangle sensor, are essentially evaluated in the reference model.Correction of the calculated desired yaw rate can be performed byadditionally taking into account the values provided by a lateralacceleration sensor.

The evaluation may be performed in various manners. One way is proposedbelow, according to which the measured lateral acceleration is firstconverted into a velocity of the side slip angle β. A correction of thedesired value for the yaw rate is performed with this value.

The calculation of β is performed, e.g., by the kinematic determinationof β 14, 15 (FIG. 2).

The procedure is carried out according to the scheme shown in FIG. 21.The estimated value of the velocity of the side slip angle β is comparedwith a first threshold value th₁ (block 400), if desired, after alow-pass filtration. The meaning of this comparison will appear onlyafter a correction of the desired value of the yaw rate Ψ_(Desired), andit is therefore explained in greater detail below.

If |β|>th₁, the value of β is compared with a second threshold value th₂(block 401), and the second threshold value is higher than the firstthreshold value th₁. If this threshold value is also exceeded,integration 402 of the velocity of the side slip angle β over time isfirst performed. To do so, the velocity of the side slip angle β ismultiplied by the loop time T₀ and added to the previous integrationresult Intg_(i-1). The integration steps are counted with n, so that thenumber n is increased by 1 after the integration (step 403). Theintegration time is thus represented by the number n of integrationsteps performed. The integration result Intg n (β) is compared with athreshold value β_(s) (block 404). The amount of the threshold valuerepresents a maximum allowable deviation from a side slip angle that istheoretically to be maintained. The threshold value β_(s) is on theorder of magnitude of approx. 5°.

If this threshold value is exceeded, the desired yaw rate Ψ_(Desired) isnewly evaluated by an additive constant S (step 405), which depends onthe instantaneous velocity of the side slip angle β and the number n ofintegration steps. This means that the desired yaw rate is furtherreduced with each new loop in which the threshold value β_(s) isexceeded. The additive constant S is either added or subtracted,depending on the sign of Ψ_(Desired), so that the value of the desiredyaw rate is reduced at any rate. If Intg_(n) does not reach thethreshold value β_(s), Ψ is not limited (step 407).

The estimated velocity of the side slip angle is checked again in arepeated loop to determine whether its value is lower than the thresholdth₁. If so, this is interpreted as meaning that the vehicle has againstabilized. The consequence of this is that n in step 406 is again setat 0 and that the further calculation in step 407 is based on a desiredyaw rate that is not corrected, i.e., it is identical to the valueobtained as the result of the vehicle reference model. In addition, thestart value Intg_(n-1) of the integration is set to equal zero.

If the value of a velocity of the side slip angle exceeds th₁, but notth₂, the old value Intg_(n) remains unchanged, i.e., the integration isomitted for one loop. The previous limitation is preserved. Should thethreshold value th₂ be exceeded again, the integration is continued.

2.4.2. Correction of M_(G)

Another possibility is to manipulate the yawing moment M_(G), which iscalculated by the control law unit 16. To do so, the difference betweenthe previous value M₁ (k-1) and the current value M₁ (k) is formed. Thesubscript 1 indicates that these values are the direct result of theyawing moment controller, i.e., they were not yet calculated on thebasis of the next correction. This difference is related to the looptime T₀ and yields ΔM₁. A correction gradient, which is obtained from βmultiplied by a correction factor, is added to this gradient ΔM₁. Thegradient thus corrected is multiplied by the loop time T₀ and is addedto the yawing moment M(k-1) of the preceding calculation. This leads tothe current moment M_(G) (k), which is used as the basis for the furthercalculation.

This calculation is performed by a logic unit as is shown in FIG. 22.The calculated moments, which are obtained from the "control law unit16" subprogram, are sent into a shift register 420. The current value M₁(k) always stands in the first place 421 of the shift register 420; theprevious value M₁ (k-1) stands in the second place 422 of the shiftregister 420. As soon as a new value M₁ is available, the value isshifted from register 421 into register 422, and the value in register421 is replaced with the new value. The values in the registers 421 and422 are sent to a calculation logic unit 430, which calculates a ΔMaccording to the following formula:

F 2.28

    ΔM=M.sub.1 (k)-M.sub.1 (k-1)+a*β*T.sub.0

In addition, the estimated velocity of the side slip angle β is sent tothe calculation logic unit 430 for this from the kinematic determinationof β. Furthermore, a value for a correction factor a, with which thevelocity of the side slip angle is converted into a change in moment, isset in a memory. The new moment M(k) is calculated according to theformula

F 2.29

    M(k)=M(k-1)+ΔM

The current value of the corrected moment is stored in register 431, andthe value from the previous calculation is stored in register 432. Thevalue in register 431 is used as the basis for the further calculation.

3. Distribution Logic Unit

3.1. Additional Yawing Moment by the Application of Brake Forces Toachieve stable travel of the vehicle even in a curve, it is firstnecessary to determine the steering angle. The steering angle representsthe curved path of the vehicle desired by the driver. In the case ofstable, stationary travel in a curve, the vehicle shall travel throughthe curve at an approximately constant side slip angle and constant yawrate. Deviations from this side slip angle or from this yaw rate must becompensated by the driver by steering in the opposite direction.However, this is not always possible when the driver travels through thecurve at the limit velocity for the curve. It is necessary in suchsituations to specifically brake the vehicle and to apply additionalmoments around the vertical axis to the vehicle, which are to bringabout an adjustment of the actual yaw rate to the desired yaw rate.

Calculation algorithms which describe this were described before, sothat they do not need to be explained in greater detail here.

However, there remains the problem that an additional yawing momentM_(G) calculated by the calculation algorithm must be put into practicein an appropriate manner by specifically applying brake forces.

In the case of hydraulic brakes, the task is therefore practically toset a brake pressure for every individual wheel brake. The moment to beobtained around the vertical axis shall be obtained with the lowestpossible pressures in the individual brakes. It is therefore proposedthat a coefficient be determined for each wheel and that the brakepressures be calculated from the vehicle yawing moment to be generatedand the actual weighted coefficient.

As was explained above, it is favorable, especially in vehicle brakesystems operating hydraulically, to determine the coefficients such thatthe brake pressure for the individual wheel brakes can be directlydetermined. The weighting of the coefficients is performed by dividingevery individual coefficient by the sum of the squares of allcoefficients.

Each coefficient determines the relationship between the wheel brakepressure and the individual wheel brake forces thus generated as apercentage of the yawing moment of the vehicle.

Parameters which change during the travel of a vehicle are included asvariables in the determination of the individual coefficients. They are,in particular,

the steering angle δ,

the coefficient of friction μ between the tire and the road surface,

the vehicle mass m, and

the axle load distribution N_(z).

Variables which are included in the calculation of the coefficients andare vehicle-specific or brake-specific are, e.g., the following, for adisk brake system:

the area A of the brake pistons,

the number n of pistons per wheel brake,

the coefficient of friction μ_(r) between the disk and the brake lining,

the ratio s of the effective friction radius to the dynamic tire radius,and

the efficiency η of the brake.

The method of calculation proposed has the advantage that thecorresponding brake pressures can be calculated very rapidly from apredetermined additional yawing moment. Should the above-describedparameters change during travel, this is taken into account via a changein the coefficients in the calculation of the brake pressure.

While some influencing variable are used linearly in the calculation ofthe coefficients, especially the dependence of the coefficients on thesteering angle δ is nonlinear.

However, it was found that a linearized estimation of the dependencebetween the individual coefficients and the steering angle yieldssufficiently good results.

FIG. 23 schematically shows a vehicle during straight travel with fourwheels 601, 602, 603, 604. A wheel brake 605, 606, 607, 608 isassociated with each of the wheels. These can be actuated independentlyfrom one another, and brake forces are generated by the wheel brakingmoments exerted by the wheel brakes on the contact surfaces of the tireson the road surface. For example, a braking force F, which in turngenerates a moment M (positive in the example) around the vertical axis,is generated on wheel 601 when the wheel brake 605 is actuated.

Such moments around the vertical axis of the vehicle can be usedspecifically to keep a vehicle stable on a path desired by the driver.

Furthermore, sensors are present in the vehicle. They include wheelsensors, which detect the angular velocity of the wheels 601, 602, 603,604. In addition, the steering wheel angle is detected with a steeringsensor 612. In addition, a sensor 613 for the yaw rate is provided.

A yawing moment, which, when applied, is able to make the yaw rate ofthe driver as well as its side slip angle agree with the driver'sdesire, can be calculated with these sensors, which detect the driver'sdesire, on the one hand, and the behavior of the vehicle, on the otherhand. The wheel brakes 605, 606, 607, 608 are actuated for this purpose,with a control device, which is part of a complex program forcontrolling the driving stability, being provided with this purpose.

The general situation is shown in FIG. 24. A program module, whichcalculates the yawing moment M_(G), is designated by 16. FIG. 24 shows acontrol device, which calculates the pressures p_(xx) that are to beintroduced into the individual wheel brakes 605, 606, 607, 608. Thepressure values 622, 623, 624, 625 determined can be subjected tofurther evaluation and can be converted into corresponding controlsignals for the wheel brakes 605, 606, 607, 608.

The control device itself consists of two parts, namely, a first part630, in which coefficients c_(xx) for the individual wheels arecalculated. The coefficients c_(xx) establish a linear relationshipbetween the pressure in the wheel brake and the proportionate yawingmoment, which is brought about by the brake force on the correspondingwheel. The individual pressure values p_(xx) 622, 623, 624, 625 arecalculated in the second part 631 by weighting the individualcoefficients and taking into account the yawing moment M_(G) to beapplied.

The pressure values as well as the coefficients are designated withsubscripts: ##EQU21##

The first calculation part 630 takes into account the steering angle,which is made available to the calculation process via an evaluation 632of the steering sensor 612. To calculate the coefficient, thecoefficient of friction μ, which is derived from the wheel rotationbehavior in an evaluation unit 633 (cf. Section 2.1.), is taken intoaccount. The wheel rotation behavior is in turn determined by a signalof the wheel sensors at the individual wheels. The mass of the vehicleas well as the load distribution N_(z), which are determined in anevaluation unit 634, in which the behavior of the vehicle is analyzed indifferent situations, are included as well. The first program part 630has access to a memory 635, which contains the above-mentionedvehicle-specific and wheel brake-specific values.

A coefficient c_(xx) is calculated from the above-mentioned values foreach wheel; the values 640, 641, 642, 643 may be calculatedsimultaneously or consecutively. The calculation is performed accordingto a function implemented in the program. The known relationshipsbetween the brake pressure and the brake force are taken into account inthis function. The relationship is usually linear. Only the steeringangle δ must be taken into account separately. How the steering anglecan be taken into account in a suitable manner will be described below.

The pressure values for the individual wheel brakes are determined inthe second calculation step 631 either simultaneously or consecutivelyfrom the individual coefficients 640, 641, 642, 643 according to thefollowing formula:

F 3.1a ##EQU22## F 3.1b ##EQU23##

Calculating the individual pressures according to this formula offersthe advantage that only relatively low pressures must be introduced intothe wheel brakes to reach the calculated braking moment. Furthermore,the brake pressure control is able to respond very sensitively andrapidly to changes especially in the steering angle and in thecoefficients of friction.

The steering angle δ is taken into account in the calculation of thecoefficients as follows: FIG. 25 shows for this a schematicrepresentation of a vehicle, in which the front wheels 601 and 602 areshown turned in. The distance between the front wheels is designated byS, and the distance between the center of gravity 610 and the front axleis designated by l_(v).

The wheel planes 650, 651 form steering angles 652, 653 with thelongitudinal axis of the vehicle. The steering angles δ 652, 653 areassumed to be equal for simplicity's sake. The effective lever arm h_(l)or h_(r) relative to the brake force F, which acts in the wheel plane650, 651, is calculated from approximation considerations for smallsteering angles as follows.

F 3.2a ##EQU24## F 3.2b ##EQU25##

Since the "small steering angle" approximation is not always satisfied,it was found to be favorable to calculate possibly with the followingformula.

F 3.3a ##EQU26## F 3.3b ##EQU27##

Should the calculated lever arms become smaller than zero, they are setequal to zero.

The wheel coefficients c_(xx) can be calculated as follows:

F 3.4

    c.sub.xx =c.sub.hydxx *h.sub.l,r,

where c_(hydxx) ∞μ·m·N_(Z) ·A·n·μ_(r) ·S·η (see definitions above) inwhich all parameters except for the steering angle δ are taken intoaccount in c_(hydxx).

The coefficients can thus be represented as the product of two terms, inwhich one term determines the effective lever arm, and the other term isindependent from the steering angle.

3.2. Additional Yawing Moment by Reducing Lateral Forces

One method of applying brake forces acting on one side is to actuate thewheel brakes such that the wheels will be braked with differentintensity. One procedure that brings this about was described in thepreceding section.

This procedure reaches a limit when a driving stability control is to beperformed during pedal braking, i.e., when a certain brake pressure hasalready been set in the wheel brakes because of braking by the driver.The above-described procedure can be applied, in principle, to this caseas well. Instead of absolute pressures, changes in the brake pressuresalready set are determined.

However, the following problems arise. If a very high pressure hasalready been introduced into a wheel brake, so that very high brakeforces are reached, an increase in the brake pressure would notnecessarily lead to an increase in the brake force, because the limit ofadhesion between the tire and the road surface has been reached. Thelinear relationship between the brake pressure and the brake force,which was assumed in the above-mentioned model, is no longer present inthis case.

The limit of the brake force on one side of the vehicle, which is not tobe exceeded, can be compensated in terms of a yawing moment control byreducing the braking force on the other side of the vehicle.

However, this has the disadvantage that the deceleration of the vehicleis also reduced with the reduction in the brake force. This is notalways acceptable, because the vehicle is to be stopped over theshortest possible distance when a braking process is initiated by thedriver. An excessive reduction in the actual deceleration of the vehiclecompared with the driver's desire cannot therefore generally beaccepted. The following approach is taken to solve this problem.

The wheel brakes of at least one wheel are actuated such that thelongitudinal slip 2 of the wheel is set such that it is greater than thelongitudinal slip at which the maximum frictional connection is reached.This procedure is based on the fact that the brake force transmitted,i.e., the longitudinal force on the tire, reaches its maximum at alongitudinal slip of approx. 20% (0%=freely rolling wheel; 100%=lockedwheel), and the brake force that can be transmitted decreases onlyslightly at values above 20%, so that there is no appreciable lossduring the deceleration of the vehicle at wheel slips between 20% and100%.

However, if the lateral force that can be transmitted, i.e., the forcethat acts at right angles to the wheel plane, is also taken into accountat the same time, a strong dependence on wheel slip is seen, which ismanifested in that the lateral force that can be transmitted greatlydecreases with increasing slip. In the slip range above 50%, the wheelexhibits a behavior similar to that of a locked wheel, i.e., hardly anylateral forces are applied.

Controlled skidding of the vehicle can be provoked by judiciouslyselecting the wheels on which a high longitudinal slip is set, and thechange in the yaw angle brought about by the skidding shall correspondto the desired change. Since the longitudinal forces are essentiallypreserved in this procedure, but the lateral forces are markedlyreduced, the yaw rate can be controlled without excessively reducing thedeceleration of the vehicle.

The wheel that is driven, at least briefly, with an increasedlongitudinal slip is selected according to the following rules. Let usexamine travel in a curve to the right, which is intended by the driver.Corresponding "mirror-image" rules apply to traveling in a curve to theleft. The case may occur in which the vehicle will not turn into thecurve as sharply as expected. In other words, the vehicle isundersteered. The rear wheel that is the inner wheel in the curve isoperated with increased slip values in this case.

However, if the vehicle turns too sharply into the curve--this case iscalled oversteering--the front wheel that is the outer wheel in thecurve is operated with high slip values.

In addition, the pressure can be prevented from decreasing on one frontwheel. This is done according to the following rules. In a drivingsituation in which the vehicle exhibits understeering behavior, thebrake pressure is prevented from decreasing on the front wheel that isthe outer wheel in the curve. The pressure is prevented from decreasingon the front wheel that is the inner wheel in the curve in a situationin which the vehicle exhibits oversteering behavior.

The actual control of the brake pressure may be performed as follows. Aswas explained before, the brake pressure in the individual wheel brakesis determined individually as a function of the yawing moment to bereached and the weighted wheel coefficients.

A factor which is independent from the brake slip can be introduced inthe calculation of the coefficients; this factor is adjusted such thatthe above-described desired brake slip will become established. Thereduction in pressure on a wheel can be limited by setting a lowerthreshold for the corresponding coefficient.

The procedure implemented in the control program of the brake systemwill be explained in greater detail below.

Based on weighted coefficients, the control program calculates the brakepressure that must be produced in every individual wheel brake. Thecalculation becomes more problematic when the vehicle is braked,especially when it is being decelerated while utilizing the limit offrictional connection between the tire and the road surface. It is quitepossible in such cases that an anti-locking control will first beginbefore a superimposed driving stability control becomes necessary.

The basic considerations for an unbraked vehicle cannot be taken over insuch cases, because, e.g., the corresponding brake force does notincrease linearly upon the increase in pressure in a wheel brake, sincethe limit of frictional connection has been reached. An increase in thepressure in this wheel brake would not consequently produce anyadditional brake force and consequently any additional moment.

Even though the same effect of generating an additional yawing momentcan be produced by reducing the wheel brake pressure of the other wheelof the axle, this would cause, on the whole, a reduction in the brakingforce, which in turn conflicts with the requirement that the vehicle isto be stopped over the shortest possible distance.

The behavior of vehicle wheels shown in FIG. 26 is therefore utilized.This diagram shows slip values λ between 0% and 100% on the X axis,where 0% indicates a freely rolling wheel and 100% a locked wheel. The Yaxis shows the frictional force and lateral force values μ_(B) andμ_(s), respectively, in the range of 0 to 1. The solid lines show thedependence of the coefficient of friction on slip for different king pininclinations. It is seen, especially in the case of small king pininclinations, that the curve has a maximum in the slip range of λ=20%.The coefficient of friction slightly decreases toward 100%. The maximumcoefficient of friction equals approx. 0.98 for a king pin inclinationof 2°, while it is still 0.93 at λ=100%. However, an examination of thevalues of the lateral force shows an extreme reduction over the sliprange, especially for great king pin inclinations. The value of thelateral force for a slip value of 0% is 0.85 at a king pin inclinationof 10, to drop to 0.17 for slip values of almost 100%.

Thus, it can be determined from the curves in FIG. 26 that relativelystrong brake forces, but weak lateral forces can be transmitted at slipvalues in the range of 40% to 80%.

This behavior of the wheel can be utilized to specifically reduce thelateral force of a given wheel of the vehicle. The wheel is selectedaccording to the following scheme, which will be explained in greaterdetail on the basis of FIGS. 27a and 27b.

FIGS. 27a,b show a schematic representation of a vehicle in a rightcurve. Corresponding to the radius of the curve and the velocity of thevehicle, the vehicle must turn around its vertical axis, i.e., theremust be a defined clockwise yaw rate.

As was explained above, the vehicle has a yaw angle sensor. If themeasured yaw rate Ψ_(Meas) deviates from the Ψ_(Desired) to be reached,an additional moment M_(G) around the vertical axis of the vehicle mustbe applied.

If the measured yaw rate deviates from the yaw rate to be reached tosuch an extent that the vehicle does not turn sufficiently, a so-calledundersteering behavior is present. An additional moment, which iscounted as negative in this situation, must be applied. It shall causethe vehicle to turn into the curve. This could be achieved in this caseby increasing the brake pressure in the right-hand wheels of thevehicle.

However, if the vehicle is already being braked by the driver, it may bepossible that these wheels already transmit maximum brake force. If thisis determined by an electronic evaluation unit, the pressure in theright rear wheel brake is increased such that the wheel runs at slipvalues in the range of 40% to 80%. Wheel 604 is therefore marked with a"λ." As was explained above, this leads to a considerable reduction inthe lateral force. Consequently, only weak lateral forces are built upon the right rear wheel, as a consequence of which the vehicle swingsout with its tail to the left, i.e., a clockwise turning begins. Theminimization of the lateral force is maintained until the actual yawrate Ψ_(Meas) corresponds to the desired Ψ_(Desired) of the vehicle.

FIG. 27b shows the situation of an oversteering vehicle. The vehicleturns around the vertical axis faster than it would correspond to acalculated desired yaw rate. It is proposed that the lateral force onthe front left wheel 601 be reduced in this case. This is also done byintroducing slip values between 40% and 80% on this wheel. Wheel 601 istherefore marked with a "λ."

A subprogram that brings about a further reduction in pressure on thefront wheel 601 (that is, the outer wheel in the curve for the case ofundersteering (FIG. 27a)) or on the front wheel 602 (that is, the innerwheel in the curve for the case of oversteering (FIG. 27b)) can beinserted in the control program for both cases. These wheels are markedwith "p_(min)." The corresponding actuations are laterally reversed fortravel in a curve to the left.

The pressure in the individual wheels can be controlled by determining acoefficient, which describes the relationship between the change inpressure and the calculated additional yawing moment M_(G), for everyindividual wheel.

These coefficients are a function of parameters that describe thevehicle or the wheel brakes, and of variables which change duringtravel. These are especially the steering angle δ and the coefficient offriction μ for the road/tire pairing (cf. Section 3.1.). A dependence onthe longitudinal slip of the corresponding wheel is now additionallyintroduced for the above-mentioned control. The pressure on individualwheels can be prevented from decreasing by defining lower limits for thecoefficients, replacing the calculated value of the coefficients withthe minimum if the actual value drops below the minimum.

A corresponding algorithm is shown in FIG. 28. The additional yawingmoment M_(G) is first calculated (program 640). The correspondingchanges in the brake force and in the brake pressure are calculated fromthis moment for the individual wheels (program part 641). The brakepressures determined are compared with thresholds p_(th), which aredetermined, among other things, by the road/tire coefficient of frictionpairing (block 642). The thresholds p_(th) determine whether a furtherincrease in the wheel brake pressure with a simultaneous increase inbrake force is possible. If the pressures to be introduced remain belowthese limit values, the control is performed according to the procedurementioned in Section 3.1. If the calculated brake pressures are abovethese threshold values, the pressures are calculated according to thescheme 644 described above.

4. Priority Circuit

The pressures to be introduced into the wheel brakes are calculated fromthe additional yawing moment M_(G) by means of a distribution logic unit(Section 3).

Based on these pressure values, control signals for inlet and outletvalves are sent by a subordinate pressure control circuit. The actualwheel brake pressures are harmonized with the calculated ones in thissubordinate pressure control circuit.

If control signals of other controllers (ABS7, TSC8, EBV9) are to beincluded as well (Section 1), it is also necessary first to converttheir control signals into pressure values by means of a hydraulic modelof the wheel brakes stored in the computer.

The pressure requirements of the YMC controller 10 are then related tothe pressure requirements of the ABS controller and other controllers.This is done in a priority circuit, which decides what requirements areto be prioritized, and whether averaged pressures are to be sent to thepressure control unit 5 for the wheel brakes. The pressure control unit5 in turn converts the pressures into valve switching times.

Instead of desired pressures, desired changes in pressure may also besent to the priority circuit (cf. Section 7).

In this case, the priority circuit 3 sends the changes in pressure Δp toits output according to the rule that the requirement to reduce thepressure on one of the wheels is preferentially satisfied, and therequirement to maintain the pressure in one wheel brake has priorityover the requirements to increase the pressure. Thus, the individualrequirements on the priority circuit are processed according to the rulethat when there is a requirement to reduce the pressure, requirements tomaintain the pressure or to increase pressure are ignored. In the samemanner, no pressure is increased when maintenance of pressure isrequired.

5. Priority Circuit with Direct Comparison of Valve Switching Times

Another method can also be used as an alternative to this.

The distribution logic unit calculates valve switching times directly,like the other controllers as well, rather than pressures, from theadditional M_(G). The valve switching times of the YMC can thus becompared with the required valve switching times of the ABS. Unlikebefore, different valve switching times rather than different pressurerequirements are then evaluated in the priority circuit.

To obtain valve switching times, the distribution logic unit firstcalculates changes in pressure to be set for each wheel brake.

Switching times for actuating the individual wheel brakes are calculatedfrom the changes in pressure by means of a downstream, nonlinear controlelement.

This nonlinear control element may be, e.g., a counter.

This counter converts the preset changes in pressure into cycle counts.To do so, the loop time T₀ is divided into approx. 3 to 10 switchingintervals (cycles). The maximum number of cycles per loop time is afixed quantity, which is determined according to the quality of controlto be reached.

How long a valve within a loop time is to be actuated is determined bythe calculated cycle count.

Since there are, in general, two valves per wheel brake, with one valve(inlet valve) regulating the feed of the pressure medium to the wheelbrake, and the other valve (outlet valve) regulating the release of thepressure medium from the wheel brake, a total of eight signals are to begenerated.

These cycle counts are sent to the priority circuit, which receives thecycle counts of other controllers in additional channels.

The priority circuit decides which controller is to be given preference,i.e., which cycle count is taken over for the actual valve control.

The response of the vehicle to the brake forces generated by theactuation of the wheel brakes is a changed yaw rate. This is detected bythe YMC controller 10, which will again determine a new additionalyawing moment.

Consequently, brake pressures are not calculated or set at any point ofthe control circuit. Therefore, the control algorithms need noinformation on the wheel brake, and, in particular, no information onthe relationship between the volume received by the wheel brakes and theresulting brake pressures.

One possibility of calculating the cycle times is explained on the basisof FIG. 29.

Brake pressures, which are to be built up in the individual wheelbrakes, are calculated from the additional yawing moment M_(G) via thedistribution logic unit 700. How this is done can be found described inSections 3.1. and 3.2. As a result of the calculation within thedistribution logic unit, there are four pressure values p₁ through p₄for a four-wheel vehicle. These variables must be converted intoswitching times for the valves, which control the feed of pressuremedium (pressure build-up) and the release of the pressure medium(pressure reduction) and from the wheel brakes.

As was mentioned above, the switching times for the valves arecalculated from the change in the preset pressure value rather than fromthe absolute values of the preset pressure value. Each value Pn (n=1through 4) is therefore sent to a shift register 701. The current valueis written to the first register place 702. The previous value from thefirst register place 702 is received in the second register place 703,so that the pressure requirement from the preceding calculation loop iswritten there. This value is designated by p_(n) *.

The current pressure requirement is read from the first register place702 in the next step 705. If this value is 0 or lower than a minimum,the program branches into a loop 706, with which it shall be ensuredthat so much pressure medium is removed from the wheel brake that thepressure becoming established becomes zero. To do so, the inlet valve isclosed and the outlet valve is opened for at least one loop time T₀.

If the current required pressure value is above this minimum, thedifference of the two register values 702 and 703 is formed. This isdone in the subtractor 707.

The calculated change in pressure Δp may be either greater or less than0. If it is greater than 0, the pressure must be increased in thecorresponding wheel brake. If it is less than 0, the pressure must bereduced in the corresponding wheel brake. In the case of a pressurebuild-up, the program runs through the right-hand decision path 710.Taking the pressure difference to be set and the pressure requirementor, if corresponding signals are present, based on the actual pressurein the wheel brake, an opening time Δt_(in) is calculated for the inletvalve. The opening time Δt_(out) of the outlet valve is set to zero.Conversely (decision path 711), the opening time Δt_(in) of the inletvalve is set to zero if a reduction in pressure is required, while theopening time Δt_(out) of the outlet valve is calculated from therequired pressure difference and the actual pressure in the wheel brakeor the required pressure, which is written in the first register place702.

As a rule, there is a linear relationship between the opening time Δtand the intended change in pressure Δp_(i).

As was explained, the calculation is performed with cycle counts ratherthan with the opening times. This is explained in greater detail in thediagram in FIG. 10. The above-described calculations are performed atconstant time intervals (loop time T₀), and the control signals for thevalves of the wheel brakes in the next loop are set as the result of acalculation. One loop time T₀ is approx. 3 msec.

Depending on how fine the control is to operate, each loop time T_(o) isdivided into N time intervals.

The diagram in FIG. 10 shows a division into 6 steps. The switchingtimes for the valves are no longer issued as time variables, but as thenumber of cycles within one loop, during which the valve is to beopened. As can be determined from FIG. 302, an opening time of 1.5 msecis obtained, e.g., for n=3.

Should the required opening time be longer than the loop time, n is setat the corresponding maximum value N (to 6 in the example shown).

This calculation is performed for each wheel brake, i.e., four times fora four-wheel vehicle. The calculations may be performed simultaneouslyor consecutively. As a result, 8 values are available; 4 values forinlet values and 4 values for outlet valves. These values are sent to amodified priority circuit 720. The switching time requirement, likewiseexpressed in cycle times, of an ABS controller and additionalcontrollers are sent to this priority circuit 720 as well.

This actuation is performed such that a change in the pressure in thewheel brakes is obtained. The pressure forces and consequently themoments exerted on the vehicle will thus change. Thus, a change isobtained in the variables which describe the driving dynamics of thevehicle. These are directly or indirectly detected by sensors and are inturn sent to the calculation.

This again leads to a changed moment requirement, which, as wasdescribed above, is converted into new control signals for the valves.

The calculation of the pressure differences to be set is based on thepressure requirements from the preceding calculation loop. However,these do not have to have been actually set, so that the actualpressures in the wheel brakes differ from the corresponding calculatedpressure requirements.

It is therefore necessary to adjust the actual pressure in the wheelbrake to the pressure requirements in certain situations. This can bedone in the simplest manner when the pressure requirement is zero, i.e.,the distribution logic unit 700 requires a value that corresponds to thepressure zero in a wheel brake. The difference from the preceding valueis not formed, and the control signals are not derived from this in sucha case, but it is branched off in step 705 into the loop 706 forcalculating the switching times, and this loop is to ensure that apressure value of zero is indeed set. This is done by setting theswitching time Δt_(out) for the outlet valve to at least the loop timeT₀. It may also become necessary to send corresponding information tothe priority circuit 720, so that this time requirement, which is tolead to zero pressure in a wheel brake, will not be superimposed bypreset values of the other controllers. In addition, it can bedetermined in this information that the reduction in pressure shall takeplace over several loop times, so that it is ensured that a completepressure reduction will indeed take place.

6. Wheel Brake Pressure Recognition

The DSC pressure controller described up to Section 4 provides brakepressure values for the wheel brakes as a result. These preset valuesmust be put into practice. One method is to measure the pressures in thewheel brakes and to compare them with the preset values. A pressurecontroller that operates according to the usual laws adjusts the wheelbrake pressure to the predetermined desired value.

This procedure requires one pressure sensor per wheel brake, i.e., fourpressure sensors for a four-wheel vehicle.

Attempts will be made, in general, even for cost reasons to make do withas few sensors as possible. In addition, each sensor represents anotherpotential source of disturbance. The failure of one sensor may lead tothe necessity to switch off the entire control system.

It is therefore proposed that an evaluation system be provided, whichderives a pressure variable that corresponds to the pressure in thewheel brakes on the basis of data available from the already existingsensors. The following concept is proposed for doing so.

As was explained above, the pressure in each wheel brake is controlledby two valves. The inlet valve controls the feed of the pressure medium,while the outlet valve controls the release of the pressure medium.

The signals sent by a pressure controller are therefore control timeswhich indicate how long a valve shall be opened or closed. One loop timeis divided into a fixed number of time intervals (cycles). The controltimes can thus be represented as a cycle count, which indicates over howmany time intervals a valve shall be opened or closed.

The basic consideration is that these control signals shall be sent notonly to the wheel brakes, but as calculated variables also to a vehiclemodel.

The real vehicle responds to the brake pressures introduced, and acertain velocity v of the center of gravity and wheel speeds ω_(i) ofthe individual wheels will become established. The velocity of thevehicle is not directly measured, but it is also derived from the speedsω_(i) of the individual wheels in special calculation steps. They aretherefore called the reference velocity v_(Ref).

Corresponding values can also be simulated within one vehicle model.

A correcting variable for the pressure in the individual wheel brakescan be determined from a comparison of the actual values of ω_(i),v_(Ref) with the calculated values of ω_(i) and v_(Ref) or on the basisof the values of ω_(i) and v_(Ref) estimated on the basis of the vehiclemodel, and a pressure calculated via a hydraulic model can be modifiedby means of the correcting variable, so that a better estimate of thewheel brake pressures can be given.

The general structure just described is explained in greater detail inFIG. 11.

A pressure control unit, which has number 5 in FIG. 1, is designated by800. The pressure control unit calculates control times for the valvesof the wheel brakes from a first value 801, which characterizes thepressure to be set, and from a second value 802, which marks anexisting, estimated or measured pressure in the wheel brake. The controltimes are represented as an output variable 803 here. The vehicle isdesignated by 810. This is to illustrate that the vehicle responds toforces which are caused by the pressures set in the wheel brakes. Thespeeds ω_(i) of the individual wheels change now as well. Wheel sensors,which detect the speeds of the wheels, so that the ω_(i) values areimmediately available, shall also belong to the vehicle 810.

An evaluation unit ω_(i) also belongs to the vehicle 810; thisevaluation unit usually represents a partial area of an ABS controller,which calculates a so-called reference velocity v_(Ref), which is tocorrespond to the actual velocity of the vehicle, from the wheel speedsω_(i) of the individual wheels under certain boundary conditions.

A slip λ_(i) can be calculated for each wheel from the individual wheelspeeds and the vehicle reference velocity.

The values ω_(i), v_(Ref) are available as output values 811. The slipλ_(i) is available as the value 812.

The calculation model used is designated as a whole by 820. It containsthree submodels, namely,

a hydraulic model 821,

a vehicle model 822, and

a tire model 823.

In two approximation formulas, the hydraulic model 821 describes therelationship between the brake pressure p and the volume V enclosed inthe wheel brake, and the change ΔV in volume when the inlet or outletvalve is opened for a certain time.

F 6.1

    p=a*V+b*V.sup.2

F 6.2 ##EQU28##

The parameters a, b and c are variables which describe the brake systemand are stored as values in corresponding memories. p describes thecurrent pressure in the wheel brake. V describes the current volumeenclosed in the wheel brake.

Δp is measured either across the inlet valve or across the outlet valve;the difference between a pressure source and p is determined in the caseof measurement across the inlet valve, while the difference between pand the pressure in a tank, which is usually 1 bar and therefore cannotbe ignored, is determined in the case of measurement across the outletvalve.

If it is assumed that the pressure in the wheel brakes and the enclosedvolume can be set to zero at the beginning of a control, the change involume and hence the change in pressure in the individual wheel brakescan be reconstructed by monitoring the valve opening times.

At any rate, it is clear that the formulas shown can describe the actualconditions only very approximately, so that a corresponding correctionis necessary.

In model 822, the vehicle is described, in general, by a rigid body,which stands on a plane in four contact points (tire contact points).The center of gravity (CG) of this body is above the plane. The distancebetween the CG and the ground is h.

The body can move in parallel to the plane, i.e., in the x and ydirections, and rotate around its center of gravity, with the axis ofrotation being at right angles to the plane of movement.

The forces acting on the body are the brake forces in the contactsurface of the tires and air resistance forces.

The wheel loads F_(z),v and F_(z),h which are directed perpendicular tothe plane can be calculated based on these considerations as follows:

F 6.3a ##EQU29## F 6.3b ##EQU30##

Such a model is usually sufficient for performing the desired pressurecorrection. The model can, of course, be refined, if necessary. For thefurther calculation, the model provides essentially the loads F_(x) ofthe tire contact surfaces as a function of the deceleration of thecenter of gravity. The wheel is considered to be a rotatable disk, whichhas a certain moment of inertia.

F 6.4 ##EQU31##

The decelerating torques acting on the wheel are determined linearlyfrom the wheel brake pressure.

F 6.5

    M.sub.Br =C.sub.Br *p

It is assumed in the tire model that the utilization of the frictionalconnection, f, namely, the ratio of the braking force to the wheel load,changes linearly with the slip of the wheel.

F 6.6

    F.sub.x.sup.˜ λ*F.sub.z

The equations given make it possible to calculate the wheel speed ofeach wheel and the reference velocity of the vehicle model.

These values can be compared with the actual values 811. This is done atthe reference point 830.

Taking a correction factor k into account, an additional volume can bedetermined from the difference between the measured and estimated speedsof each wheel.

This additional pressure medium volume ΔV is added to the calculateddesired volume to obtain the new desired volume, from which a wheelbrake pressure, which corresponds to the actual wheel brake pressurerelatively accurately, can be derived according to formula 6.1.

The accuracy of the estimation depends, of course, on the correctionfactor k, which may have to be determined by experiments in advance.

This factor differs from one vehicle to the next, and it also depends,among other things, on how well the vehicle model describes the actualconditions.

The additional volume may also include a tolerance volume, with whichthe fact that the volume throughput through the valves is notproportional to the switching times is taken into account. The openingcross section of the valve increases or decreases only slowly during theopening and closing of a valve, so that only a reduced volume will flowduring the time intervals in which the actual opening cross sectionstill increases toward or decreases from the full opening cross section.

7. Substitution of a Yaw Rate Meter

The yaw rate is a particularly distinctive variable for theabove-described control, because it is used as a controlled variable,whose deviation ΔΨ is to be minimized. However, as will be describedbelow, other controlled variables may be advantageously used as well.The following designations will be used in this section forsimplification:

Ψ_(Meas) =g_(I) as the measured actual value of the yaw rate,

Ψ_(Meas) =g_(I) as the measured actual value of the yaw acceleration,

d/dt Ψ_(Meas) =g_(I) as the measured actual value of the change in yawacceleration (yaw angle pressure).

This also applies analogously to the desired values according to FIG. 9,which are always marked with the subscript "s."

The measured yaw rate in FIG. 14 is usually determined by means of a yawrate sensor 321, which issues the output signal g_(I) However, suchknown yaw rate sensors with direct issuance of the yaw rate are of arather complicated design and therefore very expensive. This is alsotrue of the downstream comparison unit and the controller belonging tothe control circuit. It is therefore desirable here to seek a way outhere and to offer simpler sensor systems and a controller of a simplerdesign.

FIG. 15 shows the sketch of the mode of operation of a novel sensor 321,which has a first lateral acceleration meter 322 and a second lateralacceleration meter 323. The two acceleration meters 322, 323 arearranged on the longitudinal axis of the vehicle above the front axleand the rear axle, respectively. The lateral acceleration meters may bearranged, in principle, at any point outside the center of gravity SP,in which case a corresponding conversion is performed.

FIG. 15 indicates the rectangular outline 324 of a vehicle with itstires 325 and sensors. Based on this arrangement, the front lateralacceleration meter 322 measures the lateral acceleration a_(qv) at thelevel of the front axle 326, and the rear lateral acceleration meter 323measures the lateral acceleration a_(qh) at the level of the rear axle327.

The two lateral acceleration meters are able to furnish a variable thatdepends on the yaw rate. It can be shown from mathematical deductionsthat the yaw acceleration and the lateral acceleration a_(trans) of thecenter of gravity SP can be determined from the measurement results ofthe lateral acceleration meters as follows:

F 7.1 ##EQU32## F 7.2 ##EQU33##

As is apparent from FIG. 15, l_(v), l_(h) are the distances between therespective lateral acceleration meters 322, 323, on the one hand, andthe center of gravity SP, on the other hand, while v is the velocity ofthe vehicle, and β is the side slip angle. The yaw acceleration g_(I)can thus be determined from the lateral accelerations and the distancesof the acceleration meters 322, 323.

It is therefore proposed that the yaw acceleration g_(I) be used insteadof the yaw rate proposed in the previous sections, or it is alsopossible to perform a linear weighting of the individual input valuesfor the comparison unit, similarly to the prior-art condition control.The yaw rate g and the side slip angle β can be calculated from the yawangle pressure g_(I) and the velocity of the side slip angle β by meansof a band-limited integration or a first-order, scaled, low-pass filterin order to obtain variables whose dimension corresponds to the outputvariables of the vehicle reference model 302 (Section 2.3.1.) fromsensor 321.

For the band-limited integration:

F 7.3 ##EQU34## while the following dependence is obtained by using alow-pass filter: F 7.4 ##EQU35##

The velocity of the side slip angle is obtained after evaluating theequation

F 7.5

    a.sub.q =ν*(Ψ+β)

Thus, it is seen that even through a prior-art yaw rate meter can bereplaced by using two lateral acceleration meters, the measures justdescribed must be taken to transform the yaw acceleration into the yawrate. However, the measures just described must be taken to transformthe yaw acceleration into the yaw rate. After forming Δg and Δg, thecontrol law unit 16 from FIG. 1 can follow unchanged. The moment M_(G)thus calculated is additionally converted in the control law unit 16into a change in moment M by a derivation with respect to time.

However, it is more expedient under certain circumstances to pass overto a nonlinear control according to FIG. 17, in which the yawacceleration g is sent to the comparison unit 303 both as an actualvalue and as a desired value as a result from the vehicle referencemodel 302. To do so, corresponding derivatives must be formed within thevehicle reference model.

As a consequence, the deviation of the yaw acceleration Δg, rather thanthe yaw rate difference Δg, is present at the output of the comparisonunit 303 and is sent as an input variable to the control law unit 16.Furthermore, as is apparent from FIG. 17, the velocity of the side slipangle β can be additionally sent to the yawing moment control law unit16 for the more accurate determination of the change in the moment.

As was mentioned in connection with FIG. 16, it is possible to abandonan additional yawing moment M_(G) as an output signal of the control lawunit 16, and to use the change in moment M, as the output signal,instead. The change in moment, M, i.e., the derivative of the additionalyawing moment M_(G), is converted into individual changes in pressure ina modified distribution logic unit. This means that the changes inpressure are distributed among the individual wheel brakes such that thedesired additional yawing moment M_(G) is obtained, on the whole.Details of this will be described below in connection with FIG. 18.

It should be borne in mind that at the same time, there may be a certainpressure distribution in the wheel brakes due to the driver actuatingthe brake. It is more favorable in this case to determine the momentM_(G) by integrating the change in moment M, after which the pressuredifferences that must be brought about with respect to the pressureoccurring in every individual wheel brake can be directly determinedfrom the moment M_(G). The above-described advantageous variant, inwhich the derivatives of the controlled variables used in Sections 1through 3 are used, may also be combined with the distribution logicunit according to Section 3. Two control principles are available here;one of them yields an additional yawing moment M_(G), and the other achange in the additional yawing moment M as a preset value. Switchingover between the principles may be provided for. Switching over to theother control principle must be performed especially when the othercalculation of additional controlled variables (side slip angle, etc.)according to one principle cannot be performed with sufficient accuracy(cf., e.g., Section 2.2.2.). It should also be noted that Δg can also besent as a correcting variable to the control law unit 16 according toFIG. 17, in addition to Δg_(I)

Besides adapting amplifiers k1, k2, k3, two threshold value switches S2,S3 are shown in the control law unit 16 according to FIG. 17; thesethreshold value switches are to improve the control behavior within thecontrol law unit 16 and to optimally adapt the influence of theintroduced variables to the ideal control behavior as a function of thevelocity. The amplifiers k1 through k3 have a comparable task. Theindividual values are then added in an adder and sent as an outputsignal to the YMC controller 10. General explanations for the controllaw unit, which correspondingly apply here, can be found in Section 2.4.

How the pressure preset values at the output of the controllers 7, 8, 9are linked with the pressure preset value of a distribution logic unit 2in a priority circuit 3 was shown in connection with FIG. 1. The use ofpressure preset values always requires a corresponding prior conversionin the devices that issue these preset values. The effort involved inthe exchange of information between the program modules of the controlcircuit can be simplified by the measures described below.

The control circuit for controlling the driving stability according toFIGS. 9 and 14 is shown in an even more simplified form in FIG. 18; thedesignations introduced there are maintained.

The YMC controller 10 according to FIG. 1 is modified here inasmuch asthe change M in the additional yawing moment M_(G), which is sent to thedistribution logic unit 2 together with the pressure distribution on thebrakes desired by the driver (desire to brake), is present at theoutput. FIG. 14 is referred to for the calculation of M.

The distribution logic unit 2 has a logic block 340 and a pressuregradient circuit 341. The essential task of the logic block 340 is toensure that despite the intervention of the driving stability control,the vehicle as a whole is not braked more strongly than is desired bythe driver by presetting a pressure signal at the input of thedistribution logic unit 2. This is to prevent instabilities from beingadditionally introduced by the driving stability control system.Consequently, when a brake pressure is provided on a wheel based on thedriver's desire to brake, and, on the other hand, a pressure build-up onone or two wheels is required via the DSC controller and a reduction inpressure on the opposite wheels is required in order to reach theadditional yawing moment, there may be mutually contradictoryrequirements with respect to the individual wheels, namely, a pressurebuild-up with a simultaneous reduction in pressure. Regarding otherwheels, it may be required to increase the pressure not only based onthe driver's desire to brake, but at the same time also based on thestability control. The logic block ensures that the brake pressure isfirst reduced in the corresponding wheels, after which an increase inbrake pressure beyond the driver's desire up to a certain limit valuecan take place. It is thus ensured that the average brake force will notbecome greater, considering all wheels and taking the additional torquebrought about by the DSC control into account, than that desired by thedriver.

As was explained in Section 3.2., a specific increase in thelongitudinal slip λ on one wheel can be used to reduce the lateralforces, while the brake force is preserved in the longitudinaldirection. Consequently, a yawing moment can thus be generated withoutthe deceleration of the vehicle decreasing.

The changes in pressure Δp_(xx) on the individual wheels xx arecalculated in the pressure gradient circuit 341 of the distributionlogic unit 2 on the basis of predetermined constants c_(xx) and thechange in moment M, and the difference between the brake pressuredesired by the driver, P_(Brake), and the brake pressure actuallymeasured, P_(xxist), is also included in the calculation. Thus, thefollowing equation applies

F 7.6 ##EQU36## and g_(I) =proportionality factor.

The actual brake pressure p_(xxist) is determined either by a pressuregauge at the corresponding wheel, or it is calculated via a brake model,which follows the changes in pressure specified for the wheel and istherefore an image of the pressure occurring on the wheel (Section 6).The pressure requirements calculated are sent to a priority circuit 3and they are evaluated there (See section 4, above).

The above description presupposes that pressure gradients were directlyprocessed in the priority circuit. However, this is not necessary. It isalso possible to process valve switching times Δt in the prioritycircuit 3 (Section 5). However, a valve switching time circuit 343 mustbe inserted in this case between the distribution logic unit 2 and thepriority circuit 3, and valve switching times Δt will be sent by theother controllers 7, 8, 9 as well. The priority circuit now processesthe valve switching times Δt entered according to a correspondingscheme, as was described in Section 4 for the brake pressures. Theoutput variables of the priority circuit are valve switching times. Therequired changes in pressure Δt_(xx) of the individual wheels xx areconverted into valve switching times Δp according to the equation

F 7.7

    S.sub.xx =Krp.sub.xxist ·Δp.sub.xx

Here, Kr_(xx) is a gain factor that depends on the actual pressure ofthe individual wheels and is calculated during pressure build-upaccording to the following rule:

F 7.8 ##EQU37## while F 7.9 ##EQU38## applies to a reduction inpressure. Here, xx is again a subscript indicating the position of theindividual wheels.

Although the invention has been described in terms of exemplaryembodiments, it is not limited thereof. Rather, the appended claimsshould be construed to include other variants and embodiments of theinvention which may be made by those skilled in the art withoutdeparting from the true spirit and scope of the present invention.

What is claimed:
 1. Apparatus for controlling an automotive vehicle, thevehicle having a plurality of wheels which contact a surface, each wheelhaving an individually operable brake, said apparatus comprising:yawingmoment control means for determining a moment that is to be applied tothe vehicle to prevent any one of the group consisting of an undesirableyaw angle, yaw rate and yaw acceleration; slip determining means fordetermining a longitudinal slip value of each of the wheels,individually; distribution logic means responsive to the yawing momentcontrol means and the slip determining means for determining anindividual braking control operation to be applied to each respectiveone of the brakes based on said moment, including: selective actuatingmeans for selectively actuating at least one of the brakes so that thelongitudinal slip value of the wheel to which the one brake correspondsis greater than a maximum friction longitudinal slip value at which thecoefficient of friction between the wheel and the surface reaches amaximum value, without actuating all of the brakes at longitudinal slipvalues above the maximum friction longitudinal slip value.
 2. Apparatusaccording to claim 1, wherein the selective actuating means actuates oneof the brakes to a longitudinal slip value that is greater than or equalto 50% of a longitudinal slip value of a locked wheel.
 3. Apparatusaccording to claim 1, wherein the selective actuating means actuates oneof the brakes to a longitudinal slip value between approximately 50% andapproximately 70% of the longitudinal slip value of a locked wheel. 4.Apparatus according to claim 1, further comprising means for determiningwhether the vehicle is understeering,wherein one of the wheels is aninside rear wheel, and the selective actuating means actuates the brakeof the inside rear wheel so that the longitudinal slip value of theinside rear wheel is greater than the maximum friction longitudinal slipvalue, if the vehicle is understeering.
 5. Apparatus according to claim4, wherein one of the wheels is an outside front wheel, and theselective actuating means actuates the brake of the outside front wheelso that the longitudinal slip value of the outside front wheel isgreater than the maximum friction longitudinal slip value, if thevehicle is understeering.
 6. Apparatus according to claim 1, furthercomprising means for determining whether the vehicle is oversteering,wherein one of the wheels is an outside from wheel, and the selectiveactuating means actuates the brake of the outside front wheel so thatthe longitudinal slip value of the outside front wheel is greater thanthe maximum friction longitudinal slip value, if the vehicle isoversteering.
 7. Apparatus according to claim 6, wherein one of thewheels is an inside front wheel, and the selective actuating meansactuates the brake of the inside front wheel so that the longitudinalslip value of the inside front wheel is greater than the maximumfriction longitudinal slip value, if the vehicle is oversteering. 8.Apparatus according to claim 1, wherein:the distribution logic meansfurther include means for determining a respectively different weightedcoefficient for each individual brake, and an individual brakingpressure to be applied to each respective one of the brakes based onsaid moment and the respective weighted coefficient of said one brake,and at least one of the weighted coefficients is determined as afunction of the longitudinal slip value of the wheel corresponding tothe one brake that is to be actuated above the maximum frictionlongitudinal slip value.
 9. Apparatus for controlling an automotivevehicle, the vehicle having a plurality of wheels which contact asurface, each wheel having an individually operable brake, the wheelsincluding an inside rear wheel and an outside front wheel, saidapparatus comprising:yawing moment control means for determining amoment that is to be applied to the vehicle to prevent any one of thegroups consisting of an undesirable yaw angle, yaw rate and yawacceleration; understeering determining means for determining whetherthe vehicle is understeering; slip determining means for determining alongitudinal slip value of each of the wheels, individually; anddistribution logic means responsive to the yawing moment control means,the understeering determining means and the slip determining means fordetermining an individual braking pressure to be applied to eachrespective one of the brakes based on said moment, including:means fordetermining a respectively different weighted coefficient for eachindividual brake, and an individual braking pressure to be applied toeach respective one of the brakes based on said moment and therespective weighted coefficient of said one brake, the weightedcoefficients of the inside rear brake and the outside front brake beingadjusted to actuate the inside rear brake and the outside front brake,so that the longitudinal slip values of the inside rear wheel and theoutside front wheel are greater than a maximum friction longitudinalslip value at which the coefficient of friction between the wheel andthe surface reaches a maximum value without actuating all of the brakesat longitudinal slip values above the maximum friction longitudinal slipvalue, if the vehicle is understeering, and selective actuating meansfor selectively actuating at least the brakes of the inside rear wheeland outside front wheel based on the weighted coefficients. 10.Apparatus for controlling an automotive vehicle, the vehicle having aplurality of wheels which contact a surface, each wheel having anindividually operable brake, the wheels including an inside front wheeland an outside front wheel, said apparatus comprising:yawing momentcontrol means for determining a moment that is to be applied to thevehicle to prevent any one of the group consisting of an undesirable yawangle, yaw rate and yaw acceleration; oversteering determining means fordetermining whether the vehicle is oversteering; slip determining meansfor determining a longitudinal slip value of each of the wheels,individually; and distribution logic means responsive to the yawingmoment control means, the oversteering determining means and the slipdetermining means for determining an individual braking pressure to beapplied to each respective one of the brakes based on said moment,including:selective actuating means for actuating the brakes of theinside front wheel and outside front wheel so that the longitudinal slipvalues of the inside front wheel and outside front wheel are greaterthan a maximum friction longitudinal slip value at which the coefficientof friction between the wheel and the surface reaches a maximum value,if the vehicle is oversteering, and means for determining a respectivelydifferent weighted coefficient for each individual brake, and anindividual braking pressure to be applied to each respective one of thebrakes based on said moment and the respective weighted coefficient ofsaid one brake, the weighted coefficients of the inside front brake andthe outside front brake being adjusted to actuate the inside front brakeand the outside front brake.
 11. In a yaw moment control system forimproving the driving behavior of an automotive vehicle tending tooversteering or understeering, the vehicle having a plurality of sensorsfor measuring a velocity, a steering angle and a yaw rate of thevehicle, and a plurality of wheels including an inside rear wheel, eachwheel having a respective brake, a method for controlling the pressureapplied to the brakes, individually, while turning on a pavement,comprising the steps of:(a) measuring the velocity, the steering angleand the yaw rate; (b) determining a desired yaw rate based on themeasured velocity and steering angle; (c) determining a differencebetween the desired yaw rate and the measured yaw rate; (d) calculatinga moment that, if applied to the vehicle, would change the yaw rate ofthe vehicle to the desired yaw rate; (e) determining whether the vehicleis understeering; and (f) increasing pressure on the inside rear brakeif the vehicle is understeering, such that the longitudinal slip valueof the inside rear wheel is greater than a maximum friction longitudinalslip value at which the coefficient of friction between the wheel andthe surface reaches a maximum value, without actuating all of the brakesat longitudinal slip values above the maximum friction longitudinal slipvalue, thereby to maintain a longitudinal friction force between theinside rear wheel and the pavement while reducing a lateral frictionforce between the inside rear wheel and the pavement by an amountsufficient to apply the calculated moment to the vehicle.
 12. A methodaccording to claim 11, further comprising the step of decreasing thepressure on the outside front brake if the vehicle is understeering. 13.In a yaw moment control system for improving the driving behavior of anautomotive vehicle tending to oversteering or understeering, the vehiclehaving a plurality of sensors for measuring a velocity, a steering angleand a yaw rate of the vehicle, and a plurality of wheels, each wheelhaving a respective brake, a method for controlling the pressure appliedto the brakes, individually, while turning on a pavement, comprising thesteps of:(a) measuring the velocity, the steering angle and the yawrate; (b) determining a desired yaw rate based on the measured velocityand steering angle; (c) determine a difference between the desired yawrate and the measured yaw rate; (d) calculating a moment that, ifapplied to the vehicle, would change the yaw rate of the vehicle to thedesired yaw rate; (e) determining whether the vehicle is oversteering;and (f) increasing pressure on the outside front brake if the vehicle isoversteering, such that the longitudinal slip value of the outside frontwheel is greater than a maximum friction longitudinal slip value atwhich the coefficient of friction between the wheel and the surfacereaches a maximum value, without actuating all of the brakes atlongitudinal slip values above the maximum friction longitudinal slipvalue, thereby to maintain a longitudinal friction force between theoutside front wheel and the pavement while reducing a lateral frictionforce between the outside front wheel and the pavement by an amountsufficient to apply the calculated moment to the vehicle.
 14. A methodaccording to claim 13, further comprising the step of decreasing thepressure on the inside rear brake if the vehicle is oversteering. 15.Brake system for a motor vehicle with more than two wheels,comprising:braking means for braking at least some of the wheels,wherein the braking means associated with one particular wheel can beactuated independently from the others; a control device, whichdetermines the individual braking torques, which the braking means is toapply to the wheels, on the basis of a measured velocity, steering angleand yaw rate of the vehicle input to the control device, and which sendsa corresponding plurality of control commands to the braking means; ameans for determining the actual longitudinal slip of the wheels; ameans for determining a yawing moment to be generated around thevertical axis of the motor vehicle, and which sends a correspondingvalue to the control device, which is utilized to prevent one of thegroup consisting of undesired yaw angles, yaw rates, and yawaccelerations, wherein the braking means of at least one wheel can beactuated such that the longitudinal slip of the wheel will be adjustedto a value that is greater than the longitudinal slip at which themaximum frictional connection is reached.
 16. Brake system in accordancewith claim 15, wherein the longitudinal slip value to be set is greaterthan 50%.
 17. Brake system in accordance with claim 15, wherein thelongitudinal wheel slip is set to be approximately 50% to 70% of thelongitudinal slip value of a locked wheel.
 18. Brake system inaccordance with claim 15, wherein in the case of travel in a curve andan additional yawing moment that would turn the vehicle into the curve,a longitudinal slip is introduced into the corresponding rear wheel thatis the inner wheel in the curve.
 19. Brake system in accordance withclaim 17, wherein in the case of travel of the vehicle in a curve and anadditional yawing moment that turns the vehicle out of the curve, alongitudinal slip is set on the front wheel that is the outer wheel inthe curve.
 20. Brake system in accordance with claim 18, wherein:thecontrol device for each wheel equipped with a braking means determines aweighted wheel coefficient, the braking torques are determined from theadditional yawing moment and the weighted wheel coefficients, and atleast one wheel coefficient is determined as a function of thelongitudinal slip to be set.
 21. Brake system in accordance with claim15, wherein the brake pressure buildup is limited on the front wheelthat is located on the opposite side relative to the at least one wheelfor which the braking means is actuated.
 22. Brake system in accordancewith claim 21, wherein the limitation of the pressure buildup is broughtabout by a corresponding limitation of the value of the correspondingwheel coefficient.